We haven't had this situation since 1824, so its hard to say what would happen. An interesting thing to point out would be that if the GOP had won the ILL governorship and forced a compromise redraw that led to the preservation of the GOP delegation from the state, and Romney were the nominee, we would see both candidates lose their home states in such a House vote.
GOP (33): AL, AK, AZ, AR, CO, FL, GA, ID, ILL, IN, KS, KY, LA, MI, MS, MO, MT, NE, NV, NH, ND, OH, OK, PA, SC, SD, TN, TX, UT, VA, WV, WI, and WY.
DEM (16): CA, CT, DE, HI, IA, ME, MD, MA, NJ, NM, NY, NC, OR, RI, VT, and WA
Blank ballot (1): MN.
Of course it isn't the 112th but the 113th that would vote. And Dems will most certainly add ILL to their collumn as well as MN.
The Senate could be unpredictable, especially if the control is 50-50 or close to it. You might see a gang of some number of moderate Senators equally from each party created to resolve the matter.
Is it the 113th? I thought the electoral college is counted in December 2012.