At least he did in Book IV, Chapter 20 of Calvin's "Institutes of the Christian Religion." I am aware of one passage from other commentaries of Calvin's on Romans 13 which teaches something slightly different. I'll deal with that later. I'm basing this claim entirely on Calvin's teachings in Institutes.
His teachings there could not have been clearer. Based on them, the Declaration of Independence is a 100% anti-Calvinist document; that is, if "Calvinism" stopped with Calvin.
Arguably it didn't. Later "Calvinists" like Samuel Rutherford and Philippe de Mornay, apparently (and for obvious reasons) not satisfied having to live out Calvin's teachings on submitting to political tyranny, made the most out of Calvin's idea of "interposition," and expanded it in the "living" philosophical sense (i.e., "living Calvinism," "living Constitutionalism," etc.), such that results could be achieved of which Calvin himself would not have approved.
Though I'm less familiar with their works than I am Calvin's, they still, like Calvin, stopped short of approving of "revolt." Rather, if the King violated the law, since "law was King," we could follow the law not the unlawful actions of a King. That's what Rutherford taught in Lex Rex. That's NOT what Calvin taught. And even Rutherford's more generous (than Calvin's) teachings do not countenance revolt.
[Again, since I'm less familiar with Rutherford, I'll try to be cautious with claims of later "Calvinists" who expanded "interposition" beyond what Calvin taught and would have approved.]
Whatever else the Founders said they did -- i.e., "we are resisting the unlawful actions of King George and Parliament" -- something that does square with Rutherfordian rhetoric -- they said they were revolting. They used the term "revolution" over and over again to describe what they did.
So while you may be able to, as some have, analyze the events of the American Revolution as intermediate magistrates fighting a war of self defense and resisting the unlawful actions of the British, you cannot square what the Founders said they did or the rhetoric they appealed to in the DOI with such a sentiment.
And orthodox Christian critics of the pro-revolutionary sentiments contained in the DOI might note that's EXACTLY why so many "Christians" -- some orthodox some heterodox -- initially approved of the French Revolution and thought its principles an extension of the American. Once you pollute Christianity with foreign principles (like rebellion is okay) it acts as a cancer. Hence, the French Revolution as the logical extension of the anti-biblical principles of the American Revolution.
That's what, among others, Gregg Frazer, Russell Kirk, Lino Graglia, and Roberts Bork and Kraynak might note.
Now, on a personal note, to satisfy my friend Jim Babka, I am not saying the American Revolution was anti-biblical or that there aren't understandings -- even traditional orthodox understandings -- of the Bible that are compatible with revolutionary thought.
Rather, my narrow claim is 1) Calvin didn't approve this. And 2) The Founders, though some of their actions and rhetoric was consistent with more generous notions of interposition (i.e., they oft-talked about how the the British violated British law in dealing with America), went beyond that and said they revolted.
Let's look at Book IV, Chapter 20 of Calvin's "Institutes of the Christian Religion" and settle the issue. He wrote:
For while in this unworthy conduct, and among atrocities so alien, not only from the duty of the magistrate, but also of the man, they behold no appearance of the image of God, which ought to be conspicuous in the magistrate, while they see not a vestige of that minister of God, who was appointed to be a praise to the good and a terror to the bad, they cannot recognise the ruler whose dignity and authority Scripture recommends to us. And, undoubtedly, the natural feeling of the human mind has always been not less to assail tyrants with hatred and execration, than to look up to just kings with love and veneration.
25. But if we have respect to the word of God, it will lead us farther, and make us subject not only to the authority of those princes who honestly and faithfully perform their duty toward us, but all princes, by whatever means they have so become, although there is nothing they less perform than the duty of princes. For though the Lord declares that a ruler to maintain our safety is the highest gift of his beneficence, and prescribes to rulers themselves their proper sphere, he at the same time declares, that of whatever description they may be, they derive their power from none but him. Those, indeed, who rule for the public good, are true examples and specimens of his beneficence, while those who domineer unjustly and tyrannically are raised up by him to punish the people for their iniquity. Still all alike possess that sacred majesty with which he has invested lawful power. I will not proceed further without subjoining some distinct passages to this effect. 657 We need not labour to prove that an impious king is a mark of the Lord's anger, since I presume no one will deny it, and that this is not less true of a king than of a robber who plunders your goods, an adulterer who defiles your bed, and an assassin who aims at your life, since all such calamities are classed by Scripture among the curses of God. But let us insist at greater length in proving what does not so easily fall in with the views of men, that even an individual of the worst character, one most unworthy of all honour, if invested with public authority, receives that illustrious divine power which the Lord has by his word devolved on the ministers of his justice and judgment, and that, accordingly, in so far as public obedience is concerned, he is to be held in the same honour and reverence as the best of kings. [Bold mine.]
Calvin could not have been clearer: Tyrannical Kings -- even the worst that you can imagine [i.e., Hitler or Stalin] -- don't lose their Romans 13 divinely ordained status.
But there's more (the bold, again, is mine):
... When we hear that the king was appointed by God, let us, at the same time, call to mind those heavenly edicts as to honouring and fearing the king, and we shall have no doubt that we are to view the most iniquitous tyrant as occupying the place with which the Lord has honoured him. When Samuel declared to the people of Israel what they would suffer from their kings, he said, "This will be the manner of the king that shall reign over you: He will take your sons, and appoint them for himself, for his chariots, and to be his horsemen; and some shall run before his chariots. And he will appoint him captains over thousands, and captains over fifties; and will set them to ear his ground, and to reap his harvest, and to make his instruments of war, and instruments of his chariots. And he will take your daughters to be confectioneries, and to be cooks, and to be bakers. And he will take your fields, and your vineyards, and your oliveyards, even the best of them, and give them to his servants. And he will take the tenth of your seed, and of your vineyards, and give to his officers, and to his servants. And he will take your men-servants, and your maid-servants, and your goodliest young men, and your asses, and put them to his work. He will take the tenth of your sheep: and ye shall be his servants" (1 Sam. 8:11-l7). Certainly these things could not be done legally by kings, whom the law trained most admirably to all kinds of restraint; but it was called justice in regard to the people, because they were bound to obey, and could not lawfully resist: as if Samuel had said, To such a degree will kings indulge in tyranny, which it will not be for you to restrain. The only thing remaining for you will be to receive their commands, and be obedient to their words.
27. But the most remarkable and memorable passage is in Jeremiah. Though it is rather long, I am not indisposed to quote it, because it most clearly settles this whole question. "I have made the earth, the man and the beast that are upon the ground, by my great power, and by my outstretched arm, and have given it unto whom it seemed meet unto me. And now have I given all these lands into the hand of Nebuchadnezzar the king of Babylon, my servant: and the beasts of the field have I given him also to serve him. And all nations shall serve him, and his son, and his son's son, until the very time of his land come: and then many nations and great kings shall serve themselves of him. And it shall come to pass, that the nation and kingdom which will not serve the same Nebuchadnezzar the king of Babylon, and that will not put their neck under the yoke of the king of Babylon, that nation will I punish, saith the Lord, with the sword, and with famine, and with pestilence, until I have consumed them by his hand" (Jer. 27:5-8). Therefore "bring your necks under the yoke of the king of Babylon, and serve him and his people, and live" (v. 12). We see how great obedience the Lord was pleased to demand for this dire and ferocious tyrant, for no other reason than just that he held the kingdom. In other words, the divine decree had placed him on the throne of the kingdom, and admitted him to regal majesty, which could not be lawfully violated. If we constantly keep before our eyes and minds the fact, that even the most iniquitous kings are appointed by the same decree which establishes all regal authority, we will never entertain the seditious thought, that a king is to be treated according to his deserts, and that we are not bound to act the part of good subjects to him who does not in his turn act the part of a king to us.
In short, Christians are to be obedient to tyrant Kings simply because they are Kings. Obedience to tyrannical Kings is obedience to God. This is Calvin 101.
But there's even more:
But rulers, you will say, owe mutual duties to those under them. This I have already confessed. But if from this you conclude that obedience is to be returned to none but just governors, you reason absurdly. Husbands are bound by mutual duties to their wives, and parents to their children. Should husbands and parents neglect their duty; should the latter be harsh and severe to the children whom they are enjoined not to provoke to anger, and by their severity harass them beyond measure; should the former treat with the greatest contumely the wives whom they are enjoined to love and to spare as the weaker vessels; would children be less bound in duty to their parents, and wives to their husbands? They are made subject to the froward and undutiful. Nay, since the duty of all is not to look behind them, that is, not to inquire into the duties of one another, but to submit each to his own duty, this ought especially to be exemplified in the case of those who are placed under the power of others. Wherefore, if we are cruelly tormented by a savage, if we are rapaciously pillaged by an avaricious or luxurious, if we are neglected by a sluggish, if, in short, we are persecuted for righteousness' sake by an impious and sacrilegious prince, let us first call up the remembrance of our faults, which doubtless the Lord is chastising by such scourges. In this way humility will curb our impatience. And let us reflect that it belongs not to us to cure these evils, that all that remains for us is to implore the help of the Lord, in whose hands are the hearts of kings, and inclinations of kingdoms. 658 "God standeth in the congregation of the mighty; he judgeth among the gods." Before his face shall fall and be crushed all kings and judges of the earth, who have not kissed his anointed, who have enacted unjust laws to oppress the poor in judgment, and do violence to the cause of the humble, to make widows a prey, and plunder the fatherless.
In other words, you submit to the tyrant, King, parent or whomever God placed in power over you. If they treat you unfairly, God will get them for it. On Earth, the buck stops with them.
After writing this, Calvin notes examples where Kings were removed.
Herein is the goodness, power, and providence of God wondrously displayed. At one time he raises up manifest avengers from among his own servants, and gives them his command to punish accursed tyranny, and deliver his people from calamity when they are unjustly oppressed; at another time he employs, for this purpose, the fury of men who have other thoughts and other aims. Thus he rescued his people Israel from the tyranny of Pharaoh by Moses; from the violence of Chusa, king of Syria, by Othniel; and from other bondage by other kings or judges. Thus he tamed the pride of Tyre by the Egyptians; the insolence of the Egyptians by the Assyrians; the ferocity of the Assyrians by the Chaldeans; the confidence of Babylon by the Medes and Persians, -- Cyrus having previously subdued the Medes, while the ingratitude of the kings of Judah and Israel, and their impious contumacy after all his kindness, he subdued and punished, -- at one time by the Assyrians, at another by the Babylonians. All these things, however, were not done in the same way. The former class of deliverers being brought forward by the lawful call of God to perform such deeds, when they took up arms against kings, did not at all violate that majesty with which kings are invested by divine appointment, but armed from heaven, they, by a greater power, curbed a less, just as kings may lawfully punish their own satraps. The latter class, though they were directed by the hand of God, as seemed to him good, and did his work without knowing it, had nought but evil in their thoughts.
This passage is consistent with Calvin's notion that God is in charge and if a King is unfairly tyrannical, God always has the power to control events and remove the King. Calvin draws two classes of people God uses as "instruments" of His will, here. One, people who delivered from tyranny using non-sinful means, and others, who delivered from tyranny using sinful means. As Gregg Frazer has pointed out, God in His Providence, sometimes uses the sinful actions of human beings (i.e., George Washington leading an armed revolt in violating of Romans 13 and other parts of the Bible) to accomplish His will. Other times, as with Moses, no sinful means are employed. Moses led no revolt. God brought on the plagues and Moses simply took his people and left just as Pharaoh instructed.
Now, there is probably more than one way to interpret these biblical passages and if others want to make a case for righteous biblical rebellion based on these stories, I'm all ears.
Just understand: Nowhere does Calvin in Institutes use these examples to justify what he just spent lots of words telling believers was forbidden. If you see that in the above reproduced passage, you see something I don't.
Immediately after mentioning that God can take revenge on unfair tyrants, Calvin discusses what has been termed "interposition." And again, to be clear, Calvin stresses private resistance of tyrannical authority is forbidden.
... Although the Lord takes vengeance on unbridled domination, let us not therefore suppose that that vengeance is committed to us, to whom no command has been given but to obey and suffer. I speak only of private men. For when popular magistrates have been appointed to curb the tyranny of kings (as the Ephori, who were opposed to kings among the Spartans, or Tribunes of the people to consuls among the Romans, or Demarchs to the senate among the Athenians; and perhaps there is something similar to this in the power exercised in each kingdom by the three orders, when they hold their primary diets). So far am I from forbidding these officially to check the undue license of kings, that if they connive at kings when they tyrannise and insult over the humbler of the people, I affirm that their dissimulation is not free from nefarious perfidy, because they fraudulently betray the liberty of the people, while knowing that, by the ordinance of God, they are its appointed guardians.
That's the passage that later "Calvinists" like Rutherford would try to make the most of. But he gives examples of "popular magistrates" (not private men -- who as individuals have NO right to resist political tyranny) "appointed." Lower magistrates must act pursuant to recognized law, like Congress impeaching and removing the President. If there is no legally recognized mechanism for removing the tyrannical King, then tough luck.
In America in 1776, British Law was the recognized, existing law. And Blackstone -- the recognized expert on British law -- was clear that the King and Parliament (the particular way in which THEY split power) were the final EARTHLY arbiters of British law and rule.
Again, if one wants to argue, contra Blackstone, that America (the Continental Congress) was justified, as lower intermediate magistrates, in resisting the British on British legal grounds, fine. But America said it did more.
America said it revolted. And that's not consistent with Calvin, and arguable not with what the later, more generous "Calvinists" taught.