Use whatever reason you like for Jefferson dying: say a sudden severe illness. But anyway, if Jefferson had died at this point then Aaron Burr would have succeeded to the Presidency. After having already killed Alexander Hamilton.
Burr had already been dropped from the Republican ticket for the 1804 election, by the way -- so he's going to be President for less than a year. But how would the USA deal with having a President who had warrants for his arrest for murder in two of the seventeen states?
(And incidentally, who would the Republicans run as their candidate in 1804? Madison?)