I feel much alarmed at the prospect of seeing General Jackson President. He is one of the most unfit men I know of for such a place. He has had very little respect for laws and constitutions, and is, in fact, an able military chief. His passions are terrible. When I was President of the Senate, he was Senator; and he could never speak on account of the rashness of his feelings. I have seen him attempt it repeatedly, and as often choke with rage. His passions are, no doubt, cooler now; he has been much tried since I knew him, but he is a dangerous man.
Daniel Webster’s Interview with Jefferson
Thomas Jefferson was no fan of Andrew Jackson, whom he regarded as a vulgarian, a man of rashness and passion, and a duelist. They dined together at Jefferson's retreat home Poplar Forest in August 1815. Jackson was still riding high from his stunning victory over the British at the Battle of New Orleans (December 24, 1814-January 8, 1815).
Jackson was engaged in a large number of "affairs of honor," several of which found their way to the dueling grounds. On May 30, 1806, Jackson killed a man named Charles Dickinson in a duel. Dickinson had not only accused the future President of cheating him on a bet involving horse racing, but of insulting Jackson's wife Rachel, whom Dickinson called a bigamist.
Jackson's "Americans" appeared in force at his first inauguration on March 4, 1829. After the ceremony, the first held on the East Portico of the Capitol, the mob forced its way into the White House, climbed through windows, stood on the furniture, and tore down draperies. In order to clear the White House, bowls of punch and other hard liquors were place on the front lawn.
Needless to say, this was not the sort of dignified republic Jefferson had in mind. He was, all of his life, fearful of the role of popular military leaders in the governance of a free society.
Given that, plus Jefferson's antagonism to paper currency, I doubt that he would lose much sleep over the removal of Andrew Jackson from the $20 bill. Jackson displaced Grover Cleveland on the $20 back in 1928.
Whether he would be in favor of replacing Jackson with Harriet Tubman (ca. 1820-1913) is another question, of course.
Like most Virginia slaveholders, Jefferson lived in fear of a general slave revolt, and helped to put down such minor revolts as that of Gabriel Prosser in 1800. Jefferson placed newspaper ads offering rewards for Monticello slaves who ran away. He regraded slavery as a nightmare and a violation of natural rights, but somehow managed to learn to live with the institutional all of his life. He freed only eight slaves: three in his lifetime, five at the time of his death in 1826. He would have been against the Underground Railroad (an anachronistic term for TJ).
Jefferson never met Harriet Tubman. It's not clear what she would have thought of Jefferson. Because he had written a passionate denunciation of slavery in Notes on the State of Virginia, he was often cited by abolitionists who, without forgetting that he was a lifelong slaveholder, nevertheless regarded Jefferson as an ally of careful manumission, a statesman (stuck in an institution he despised) who had the right core values on this subject. This probably gives Jefferson more credit than he deserves, but rhetorically speaking, he could be quoted as an abolitionist.
Jefferson would have preferred that money be stamped on precious metals, which have intrinsic value anywhere in the world. He feared that paper certificates could be manipulated by the "Hamiltonians," since the value of any bill ($1, $2, $100) is only what the government and the economy ascribe to it; otherwise, it is mere printed paper.
But if we must have paper currency, Jefferson would surely have preferred that we remove all visages of historical figures from our bills, to be replaced by such things as celebrate the beauty and sublimity of America, the new Garden of Eden. Perhaps the Natural Bridge in Virginia; the Confluence of the Shenandoah and Potomac at Harper's Ferry; the Great Falls of the Missouri River (discovered by Jefferson's protege Meriwether Lewis); the Source of the Mississippi; the Grand Canyon; etc.
In my own view, we should follow Britain and Europe's lead in placing cultural giants on our currency. Britain's decision in 2013 to place Jane Austen on the 10 pound note seems just right. What about Emily Dickinson, John Muir, Aaron Copland, Louis Armstrong; Mark Twain, Zora Neale Hurston, Henry David Thoreau, William Faulkner, or for that matter Harriet Tubman?
People often ask me what Jefferson would think about being on the seldom-used $2 bill. I doubt that he would care much, but he would not feel honored. The Library of Congress—now that's a proper tribute to Thomas Jefferson.