Sabato's Crystal Ball outlines one scenario:
The simplest way to explain this scenario is that Obama retains all the states John Kerry won in 2004, while adding New Mexico and Ohio. Under the 2004 map, that would make Obama president. But the 2010 reapportionment sent a handful of electoral votes from the Blue states to the Red states: just enough to make this scenario an exact 269-269 tie. But 269 would make Romney president, because in the event of a tie, the new House of Representatives would pick the president: each of the 50 delegations would get a single vote. Given that Republicans are almost assuredly going to control a solid majority of House delegations in the next Congress (see below), Romney would win.
They pray this doesn't happen:
We don’t have a dog in this race, but we are rooting for one thing: no tie! A 269-269 Electoral College outcome would inevitably be a national crisis on par — or worse — with the 2000 Florida cliffhanger, especially if Romney lost the popular vote.
A review of electoral tie rules here.