Here's a hypothetical. Republicans win the house and senate. They pass a budget that is $3T, or at least $600B less than the current budget. Obama vetoes it. Republicans can't override it and refuse to pass continuing resolutions to pay for government at the $3.6T level. So govt. shuts down, like it did under Clinton. Who deserves the blame? Let's throw a little monkey wrench into the scenario. The republicans attach to the budget to continue the bush tax cuts except on the highest earners, as Obama wishes. Who deserves the blame for shutting down govt. in this case?
They both (Obama & the House) do. Then, hopefully, they get together like sensible people and settle on a compromise. Lastly, if the GOP does actually take control of the House and then pulls a cheap stunt like that, it'll be a short two years that they govern.
But if the Republican's own the house, wouldn't that mean that Obama isn't the people's choice any longer? As for who's fault it would be, I would probably blame both parties. I think Obama's budget is ridiculous, but I also don't think the republicans should attach any of the Bush tax cuts to it.