Could the 2012 presidential election result in a tie in the Electoral College?
Yes, and the scenario -- while unlikely -- isn't wildly improbable either.
In order to be elected president, a candidate must win at least 270 electoral votes. If you tweak the potential results in 7 battleground states, for example, and assume no surprises in those places already assumed to be in one column or the other, you can get to a 269-269 tie.
Three states with 22 electoral votes (Iowa, Nevada, and Wisconsin) would have to be in the Obama camp (all are thought to be leaning that way), while four states with 69 electoral votes (Colorado, Florida, Ohio, and Virginia) would have to be in the Romney camp. Of these 4 only Florida appears to be leaning toward Romney, but all are very close.
Here is the state-by-state breakdown, under this scenario. The 7 battlegrounds are marked with an '*' (sorry if the formatting is wonky):
California 55 Alabama 9
Connecticut 7 Alaska 3
Delaware 3 Arizona 11
D.C. 3 Arkansas 6
Hawaii 4 Colorado* 9
Illinois 20 Florida* 29
Iowa* 6 Georgia 16
Maine 4 Idaho 4
Maryland 10 Indiana 11
Massachusetts 11 Kansas 6
Michigan 16 Kentucky 8
Minnesota 10 Louisiana 8
Missouri 10 Mississippi 6
Nevada* 6 Montana 3
New Jersey 14 Nebraska 5
New Mexico 5 New Hampshire 4
New York 29 North Carolina 15
Oregon 7 North Dakota 3
Pennsylvania 20 Ohio* 18
Rhode Island 4 Oklahoma 7
Vermont 3 South Carolina 9
Washington 12 South Dakota 3
Wisconsin* 10 Tennessee 11
West Virginia 3
Total 269 Total 269
The 12th amendment to the Constitution is quite clear about what would happen next. The presidency would be decided by the newly elected House of Representatives, with each state delegation casting one vote. Barring a highly unlikely Democratic takeover of the House tomorrow, the end result would almost certainly be a party line vote in favor of Mitt Romney. While Obama's support largely comes from the most populous states, Romney would have support from a higher number of states. And even in some of the states Obama is likely to win -- like PA, OH, and WI -- the majority of their House delegations are Republican.
It would be quite something, no question, if this were the result -- among other things, it might be incredibly destabilizing politically, particularly if a case could be made that GOP voter suppression efforts (voter ID laws) played a role in swinging even one state (Florida would be, once again, the most likely culprit). Of course, if that case cannot be legitimately made, the Constitution says what the Constitution says, and Mitt Romney would rightfully become the 45th president.
Perhaps the strangest part of this whole scenario actually involves the selection of the vice-president. The Senate makes this decision, which at first blush appears to mean that Romney would be joined by Joe Biden. However, the 12th amendment (and Senate rules) are silent on whether a minority of US Senators could use the filibuster to frustrate the will of the (Democratic) majority. If the Senate parliamentarian allows the use of the filibuster, the presiding officer of the Senate (who would be, of course, VP Biden) could ignore that advice, and call for a straight-up vote.
Which could result in a 50-50 tie. However, unlike other decisions over which the Senate regularly presides, Biden could NOT then break the tie. The 12th amendment calls for a majority.
No one knows what would happen at that point. Presumably they could continue to deliberate, until 1 person changes their mind. It is possible some other individual -- not Joe Biden, and not Paul Ryan -- could be selected, if 51 senators could agree.
There will, of course, be a great deal of pressure for the Senate to select Ryan, since the House will decide first. But if Obama-Biden won the popular vote on Election Day, there will also be a great deal of pressure to select Biden. One probably shouldn't discount the fact that Biden was a US Senator himself for a very long time, and has many friends on both sides of the aisle.
That said, I think this scenario is extremely unlikely, because Colorado and especially Ohio are most likely going to wind up in Obama's column. Obama also holds a small but steady lead in the polls in Virginia, and demographic changes since 2008 make a surprise Obama victory in Florida a decent possibility too.
One should also keep in mind that there still are a couple of states (Maine, Nebraska) that allow the splitting of electoral votes. While this is unlikely, its not impossible, and it could break the deadlock before it gets to the House (most likely in Romney's favor).