I just discovered that majority of quotations from Palin's "Christian Heritage" resolution are misquotes. The actual underlying quotations do exist. She doesn't cite them exactly as they are in the originals. When scholars want to do this, they have to use ellipses "..." and brackets  or else they make an error [sic]. Most of Palin's quotes are copying errors.
Let's break down her resolution beginning with the first quotation by Ben Franklin:
WHEREAS, Benjamin Franklin, at the Constitutional Convention stated, "It is impossible to build an empire without our Father's aid. I believe the sacred writings which say that, Except the Lord build the house, they labor in vain that build it (Psalm 127:1)."
This misquotes Franklin's speech at the Constitutional Convention [as recorded by James Madison] where he was recording as saying:
I have lived, Sir, a long time, and the longer I live, the more convincing proof I see of this truth that God Governs in the affairs of men. And if a sparrow cannot fall to the ground without his notice, is it probable that an empire can rise without his aid? We have been assured, Sir, in the sacred writings, that “except the Lord build the House they labour in vain that build it.” I firmly believe this; and I also believe that without his concurring aid we shall succeed in this political building no better, than the Builders of Babel:
Next Palin writes:
WHEREAS, George Washington enunciated, "animated alone by the pure spirit of Christianity, and conducting ourselves as the faithful subjects of our free government, we may enjoy every temporal and spiritual felicity."
This misquotes an address Washington gave to Roman Catholics by a few words, notably switching "ourselves" for "themselves." The bold is mine:
And may the members of your society [the Roman Catholics] in America, animated alone by the pure spirit of christianity, and still conducting themselves as the faithful subjects of our free government, enjoy every temporal and spiritual felicity.
Next Thomas Jefferson. Palin writes:
WHEREAS, Thomas Jefferson, author of the Declaration of Independence, wrote, "Can the liberties of a nation be secure when we have removed the conviction that these liberties are the gift of God?"
This misquotes Jefferson's "Notes on the State of Virginia" where he said:
And can the liberties of a nation be thought secure when we have removed their only firm basis, a conviction in the minds of the people that these liberties are the gift of God? That they are not to be violated but with his wrath? Indeed I tremble for my country when I reflect that God is just: that his justice cannot sleep for ever . . . ."
In her defense, though, the words "Can the liberties of a nation be secure when we have removed a conviction that these liberties are the gift of God?" do appear on panel three of the Jefferson Memorial.
Next Madison, Palin writes:
WHEREAS, James Madison, father of the United States Constitution advocated "the diffusion of the light of Christianity in our nation" in his Memorial and Remonstrance.
What the Memorial and Remonstrance actually says:
12. Because the policy of the Bill is adverse to the diffusion of the light of Christianity. The first wish of those who enjoy this precious gift ought to be that it may be imparted to the whole race of mankind.
The George Mason quotation from the Virginia Declaration of Rights is accurate. And I haven't been able to confirm the Patrick Henry quotation in the original record.