That is a very interesting question. The breakaway from the Whig party became the Republican Party which nominated and elected Abraham Lincoln. The Republicans held the White House for the next 24 years. That's possible again, but not with any of the current GOP candidates.
The more likely outcome is another 8 years (maybe more) of Democratic Presidents.
Yeah, another 8 years of nothing new is probably likely. Of course the tea partier's could always show off their juvenile stripes by revolting to become some other reformed party; or take over some minor party like the American Freedom Party.
At another level, it is hard to say as when thing start to rupture, events can happen very rapidly. The House can remain fractured/chaotic, and generally a large portion of House seats could be retained by either party simply by the big R or D on the ballot next to the candidate. If the mainstream Repugs think the Senate cannot be won again, w/o jettisoning the tea partiers, change might start happening within their party. Right now the Repugs still retain the Senate, and will probably retain the ability to win/retain control for at least 2 more presidential cycles. But with the US shifting demographics, the Repugs are being bled by 2 percentage points of white voter makeup every 4 years. And in 8 years that will especially matter in Texas as Hispanics edge very close to being the majority (though maybe not as a percentage of active voters yet).