Actually, Thomas Jefferson co-founded the political party that is now known as the Democratic Party:
"Jefferson started the Jeffersonian Democrats aka Democratic-Republic, (forerunner to the Democratic Party). They were the second political party, after the Federalist. Sadly, Jefferson used others, (ie newspapers loyal to him), to try and discredit Washington's policies during his second term."
It would seem, then, that Thomas Jefferson was a Democrat, and Washington did not believe in political parties and was a member of no party. The modern Republican Party was not founded until 1854, shortly before Lincoln became President. What was called the "Democratic-Republican Party" back in the late 1700s and early 1800s split into two parties in 1824 and the Republican wing (called the National Republican Party) became defunct and was succeeded by the Whig Party.