I've long believed that unless the Democrats really change something, they are likely to be marginalized, while the Republicans will split in two, with the two pieces dividing the remnants of the Democrats in some way until the natural near-50/50 equilibrium of our system is restored.
Something's going to trigger that, but I don't think immigration is going to be it. If an issue doesn't come close to splitting the party 50/50, then the Republicans will just follow the issue. I don't think Republican voters are anywhere near 50/50 on this. The third party will be offered some concession, and stripped of their major issue (if it's immigration), they'll take it unless they're stupid.
Money talks, but ultimately only because it can buy votes. While the Congressional Republicans may feel like they can tell their constituency to take a long walk off the short pier at the moment, if they truly have to choose between re-election and continued support from the pro-illegal-immigration interests, re-election will win handily.
I still think it's the fiscal conservatives and the libertarians that are more likely to break off.
I'm also not convinced that "supporting a third party" is a very good strategy for the Democrats either, regardless of the third party's platform. By definition, this third party's platform will be non-Democratic. The Democrats will be balancing on the razor's edge between "weakening the Republicans enough to win" and "creating two viable American political parties that aren't Democratic", making them the third wheel in a system extremely strongly biased towards two dominant parties. It's only appealing if you ignore the fact that there's a real possibility of complete loss.
Update April 14: Of course, that opinion is predicated on the idea that the Republicans would wake up at some point and smell the rebellion in their base. If that's going to happen they sure are taking their sweet time about it.
Coming from the other side, there's the Euston Manifesto, which I basically see as some people who think of themselves as Left waking up and realizing that an awful lot of the issues that currently belong to "the Right" really belong to them, historically speaking; right now, the "Classical Liberals", which I consider myself to be, aren't completely at home on "the Right" or "the Left" right now. At the moment they are more at home on the right, but that's anomalous.
Whether or not a third party does well in 2008 is entirely in the elected Republican's hands right now. If they wake up, then they may come away yet stronger. If they don't, then a third party in 2008 is a real possibility. And you know what? People talk as if the third party is an automatic Republican spoiler. I say, Perot really didn't lose by that much in absolute terms. I say the third party can win, if they play their cards right.
Personally, I'm all in favor of that, because if the third party comes out based on the current political fault lines, I will be far more aligned with it than either Republican or Democrat. Might even be motivated to do some volunteering for it, something I'd really never dream of with either current party.