What WorldNutDaily and a few others are doing.
It's certainly true that Jefferson and the United States had problems with Muslim terrorists of their day -- pirates. And it may be true (I haven't yet confirmed it) as WND asserts,
The Continental Congress then met in 1784 to talk about treaties with leaders of the region, and John Adams, Thomas Jefferson and Benjamin Franklin were appointed to oversee the work.
"Tribute" and "ransoms" first were paid to the Muslim slavers, and Adams argued that was the cheapest way to get commerce moving, Sampley wrote. But Jefferson was opposed, proposing a settlement of the issue "through the medium of war."
Sampley writes that two years later, when Jefferson was ambassador to France, and Adams was ambassador to Britain, they met in London with Sidi Haji Abdul Rahman Adja, the ambassador to Britain from the "Dey of Algiers."
Seeking a peace treaty, based on Congress' vote to pay tribute, the two Americans asked Dey's ambassador why Muslims had so much hostility towards America. They later reported to Congress the ambassador told them Islam "was founded on the Laws of their Prophet, that it was written in their Quran, that all nations who should not have acknowledged their authority were sinners, that it was their right and duty to make war upon them wherever they could be found, and to make slaves of all they could take as Prisoners, and that every Musselman (Muslim) who should be slain in Battle was sure to go to Paradise."
But it is most certainly not true that those three Founders took the quoted ambassador's comments as representing authentic Islam. That's the spin that WND following Gary Demar gives this history:
"So what did Jefferson learn from the Quran? …Unless a nation submitted to Islam, whether it was the aggressor or not, that nation was by definition at war with Islam. It's no wonder that Jefferson studied the Quran. He realized that if Americans ever capitulated, the Muslims would be singing 'From the Halls of Montezuma to the Shores of A-mer-i-ca,'" DeMar concluded.
I've studied Jefferson's (and Adams' and Franklin's) writings on religion in detail, and I can attest that they registered no such complaint about Islam. In fact, they didn't often talk about Islam, but when they did we get the impression that they believed such a system was exactly like Christianity: it contained seeds of truth and a whole lot of corruption. These three Founders were, like or not, theological universalists who believed that all world religions of which they were aware (including Islam) were, at heart, valid paths to God. Perhaps it was this underlying premise (which many theologians think absolutely erroneous) that blinded them from seeing the "truth" about Islam, but it is what they believed.
The following is one of the few times in Jefferson's personal letters where he discusses Islam and he views its violence and corruption as being on par with Christianity's. From his September 27, 1809 letter to James Fishback:
Every religion consists of moral precepts, and of dogmas. In the first they all agree. All forbid us to murder, steal, plunder, bear false witness &ca. and these are the articles necessary for the preservation of order, justice, and happiness in society. In their particular dogmas all differ; no two professing the same. These respect vestments, ceremonies, physical opinions, and metaphysical speculations, totally unconnected with morality, and unimportant to the legitimate objects of society. Yet these are the questions on which have hung the bitter schisms of Nazarenes, Socinians, Arians, Athanasians in former times, and now of Trinitarians, Unitarians, Catholics, Lutherans, Calvinists, Methodists, Baptists, Quakers &c. Among the Mahometans we are told that thousands fell victims to the dispute whether the first or second toe of Mahomet was longest; and what blood, how many human lives have the words 'this do in remembrance of me' cost the Christian world! We all agree in the obligation of the moral precepts of Jesus; but we schismatize and lose ourselves in subtleties about his nature, his conception maculate or immaculate, whether he was a god or not a god, whether his votaries are to be initiated by simple aspersion, by immersion, or without water; whether his priests must be robed in white, in black, or not robed at all; whether we are to use our own reason, or the reason of others, in the opinions we form, or as to the evidence we are to believe. It is on questions of this, and still less importance, that such oceans of human blood have been spilt, and whole regions of the earth have been desolated by wars and persecutions, in which human ingenuity has been exhausted in inventing new tortures for their brethren. It is time then to become sensible how insoluble these questions are by minds like ours, how unimportant, and how mischievous; and to consign them to the sleep of death, never to be awakened from it. ... We see good men in all religions, and as many in one as another. It is then a matter of principle with me to avoid disturbing the tranquility of others by the expression of any opinion on the [unimportant points] innocent questions on which we schismatize, and think it enough to hold fast to those moral precepts which are of the essence of Christianity, and of all other religions.