First a caveat: I don't know much about USA politics, so some of my suggestions might not fit. With that in mind...This is actually an FH misc question, but we don't have a misc thread for FH, so I'm sticking it here:
I'm looking for two relatively generic names for alternate US political parties. They don't have to be quite as generic as 'Democrat' and 'Republican' but I'm looking for something that isn't nearly as descriptive as is typical for European (or smaller US) parties - for example, you know what the Greens stand for just by their name, you know what the Social Democrats stand for, just by their name, and (in countries where the word still has the same connotations as in the 19th century) you know what the Liberals stand for, just by their name.
At the moment, I have the Continental and Federal (or Continentalist and Federalist) parties.
How about the National Party? That could stand for anything the party wants it to. Similarly the Union Party or, combining them, the National Union Party (though I see from from this wikipedia page that there was an N.U.P. in the 19th C and a U.P. in the 1930s, so maybe not.)
Alternatively, some countries have parties named after famous dates, so if that fits with your story you could have the 4th of July Party.
There's also the possibility of naming a party after its founder or someone the party claims as its 'real' founder based on ideology (whether that's true or not), e.g. the Hamilton Party, Roosevelt Party or Reagan Party.
You could also just append New to an old party name, e.g. the New Democratic Party or New Alliance Party, etc.
I assume you want to avoid names like the Freedom Party or People's Party as too descriptive (even though they could actually represent any number of ideologies). That probably applies to Patriot Party too (and a party with that name actually existed, from the 1960s to 1980, too). Though if it works with your story, either it or the Patriotic Union Party might work.
Action Party might work too, as something generic promising almost anything.
That post ended up longer than I thought it would...