AHC/WI: Surviving Federalist Party?

As the title states, how could the Federalist Party have survived as a national party through the 19th century and perhaps up the modern day, and what effects would that have on the United States?
 
the federalists basically became the National Republicans, then the Whigs, then most northern whigs became republicans, everyone in the south became a democrat

then between 1896 and 1980 the democrats and the republicans basically swapped political positions, with the democrats becoming more liberal and the centre-left party and vice versa

for the first party system to be preserved, maybe just have Jefferson elected in 1796, without the disaster of the John Adams presidency, the federalists might have had a chance, once the Virginia dynasty of presidents (Jefferson, Madison, Monroe) had all served
 
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