Do you think that the Democrat and Republican parties will become a third party?

[Storebought]

No. Only the loser countries of the world have political parties that dissolve over a single issue (Ex. Canada's "Progressive Conservatives"). Americans political parties are made of tough shi(r)t.

Consider the GOP. After Watergate and the 1974 midterms commentators wrote off the GOP as a minor (not minority) party. Two years later, Ford lost to Carter by over a million votes, thus seeming to confirm the GOP's minor party status. But in 1980, the Republicans won a majority of the vote running against two parties!

Never dismiss the strength of the American voter.

[Storebought]

Correction: the PC party did *not* dissolve over a single issue.
It split three ways (PC, Reform (later CA), BQ). The PC's and the CA have recently merged.

You do realise that a political party splitting three ways is the equivalent of dissolution.  How many voters will care about the differences that separate one tendon from a dead party versus another tendon from the same dead party? They don't. In Canada, they just vote Liberal and be done with it.