Third parties do one of four things:
1. Die or remain irrelevant. Hello, Libertarian Party!
2. Kill an existing party. You don’t see the Whigs around anymore.
3. Vote-split and re-merge, the obvious example being the Canadian schism of the Reform wing from the Progressive Conservative party in 1993, which was re-formed twelve years later into the new Conservative Party, or
4. Permanently shift the other parties.
The question is which of these 4 the new Conservative Party would do. Obviously, the LIKELIEST answer is 1.
But if this gains any traction, I think Der Trihs is right, and it’ll be 3. They’ll vote-split with the Republican Party for awhile until a resolution is finally come to and they re-form as a unified conservative party.
What I think is less likely, but would be inteesting nonetheless, is Option 4; the Conservative party assumes a stance on the right wing, leaving moderate Republicans to shift to the centre, and pushing Democrats off the centre and into the left. In all likelihood that would mean that in the long term the Republican Party would become the preeminent party, after a period of a few decades in the wilderness. Unlikely, but the scenario’s possible.
It’s interesting to note what happened in Canada. The NDP aside, going into 1993 you basically had two parties that could win a national election; the Liberals and the Progressive Conservatives. You can consider them Democrats and Repubpicans for the purpose of this exercise, although that’s not really a very accurate comparison in terms of the issues. The PC party had the Reform Party, a more socially conservative (but institutionally very willing to change things, as their name indicates) wing, split off. The result was vote split and total Liberal domination for a decade. But when the Reform and PC parties got back together to become the Conservative Party, the combined party started trouncing the Liberals. Now, this might be coincidence - it is certainly true that the Liberals have had unimpressive leaders at the same time the Conservative Party re-formed - but there’s no doubt a unified party was a more attractive voting option.
The new Conservative Party, of course, is a party of compromises; it maintains is popularity and election-winninjg capability by conceding a lot of issues to appeal to moderate voters. (Their unwillingness to even allow their memebrs to say anything about gay marriage or abortion being obvious cases; the party’s leader is personally opposed to both but politically will touch neither with a fifty-foot pole.) This pisses off the party’s very socially conservative members, but the party has enough political capital to do it and still win their votes. Who else they gonna vote for?
A Republican schism would likely result in the same thing; for awhile the Democrats will clean up. If the parties eventually merge, doing so will require compromising away at least some of their more extreme positions on things like abortion and gay marriage and obsession with Christianity, and the unified party will suddenly become a viable voting option for many who previously would not have voted for them.
Option 2 is so unlikely as to be impossible, I suspect.