The neocons will leave first. As religious conservatives will rediscover their noninterventionist roots. Fiscal cons will be infused by libertarians leaving neocons nowhere to go but make their own party.
I'll go with this...but no one is starting a new party without one of the major parties being totally locked out of power for three elections in a row...say Romney sweeps with large coatails in 2012 and the Dems can't make any inroads back into congress or the White House by 2020...then, the various elements of the party might try to form a third party on a different "Antirepublican" ideology that makes up a better opposition. On the other hand if Romney loses by enough and the Democrats are able to retake the house by 2014 or 2016 and Romney's succesor still loses and Democrats get reelected in 2018, the Republican Party's existence may be questioned.
The only real exception to this rule was in the 30s and 60s, but that simply was because there were enough DINOs to give Minority Republicans a chance to influence policy and before that when the Democrats were unpopular, they still had Monolithic control over the South and the big cities to continue to justify their existence. Neither party has that much monolithic support (70%+) and both parties are pretty consistent.
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