They probably will, much to their peril. As has been mentioned, Burris gives the Republicans the best shot in a blue Illinois due to a bruising primary fight among the Democrats. If Burris is ousted, then the Lt Governor, who is untainted by "Blago-gate", would appoint a Democrat who would also be untainted, who would subsuquently cruise to election in 2010 all other factors being equal.
I say go for it Republicans, but you'd be doing it at your own risk, and to the benefit of Harry Reid.
If the Republicans expel Burris, they would probably also dramatically help Sen. Reid and let him focus on his job and his constituency rather than worrying about a pain such as Burris, thus turning what should be a lean-Democratic seat into a safe-Democratic seat in Nevada. So, they'd lose the possibility of taking one, possibly two, seats from the Democrats in 2010.
It would be kind of a two-fer for the Democrats if the Republicans get rid of Burris.
The GOP is obsessed with getting a special election, why wouldn't they just insist upon that like I said in the post before you? In fact, I'm 99% convinced that's what they would do. A special election is far more likely to elect a Republican because Mark Kirk would not have to give up his House seat to run and the recent Democratic fiasco would be more recent memory.
It'd be easy for them to publicly argue that Democratic governors in Illinois shouldn't be allowed to pick yet another Senator.
PLUS, Burris won't firmly come down in support for the Employee Free Choice Act