In 2012, the U.S. presidential election will be contested with a new electoral college (538 votes), based on the redistribution of congressional seats (435 of them) according to the 2010 U.S. Census. However, in the event of a tie (269-269) the back-up system for electing the President kicks in.
The current House of Representatives at the time of the 2012 election, that's the people who are elected next month, will have to decide on a state-by-state basis, which candidate they want to win. For example, Delaware, which has one Representative, will have one vote decided by that representative, but California, which has 53 Representatives will have it's one vote decided by a vote of the 53 delegates.
It's worth noting that if the 2012 election were today and the current House of Representatives members were choosing, then the partisan breakdown would be Democrat 32 votes, Republican 16 and a tie for Hawaii and Idaho.
Using Nate Silver's Fivethirtyeight.com most recent forecast of the House elections, I've drawn up a spreadsheet showing how the latest forecasts could tip the state delegation counts.
Assuming the election goes according to the current estimates (which is unlikely, because things are bound to change at least a little in the next couple of weeks), we could see a switch to 29 Republican votes, 18 Democrats and three tied (Idaho again, Mississippi and New Hampshire).
If I were advising the Democrats on where to throw any extra cash lying around for this election, I'd pick the close contests in the following states:
Arizona, Colorado, Mississippi, Nevada, New Hampshire and West Virginia. I wouldn't spend too much, because the odds of a tie in the electoral college are very low. Also, there are too many seats in play to defend adequately, to some extend luck and local resilience is needed.
If you want the specific seats I'd defend, here they are: AZ8 and possibly AZ5; CO3; MS4 (to keep the tie); NV3; NH2 (to keep the tie); and WV1.