Surely the party leaders would come together and make a compromise, something like a Romney/Biden administration, but Romney appoints several Democrats to the cabinet and agrees not to repeal Obamacare.
Why would the GOP compromise, if they have the numbers in the House to take the presidency? They'd elect Romney in the House, and (if the Dems still have a majority in the Senate) the Senate would make Biden VP. Biden would of course be shut out of Cabinet meetings and the like, and would spend all his days presiding over the Senate, and acting as the 101st Senator.
The aftermath of the election and the leadup to both the electoral vote and the vote in the House would be a huge media circus, akin to the 2000 election fiasco. There would probably be some faithless electors (some Ron Paul ninjas, perhaps), but none who would crossover and vote for the other party, which means that there'd still be no EC majority, and it would still go to Romney in the House. The National Popular Vote compact would gain some traction, and there'd be a renewed push to pass it in state legislatures around the country, but GOP opposition to it would harden.
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