We talked about this topic 3 weeks ago, when Nate Silver speculated about it (and noted that the constitutional method for producing an outcome is quite likely to give the election to Romney). At the time, Silver said it was "quite unlikely":
Of the 25,001 simulations that we ran on Monday, a 269-269 tie came up in 152 model runs, or about 0.6 percent of the time.I have no idea what the probability is now, but I'm sure Silver could run thousands of simulations and wow us with a very specific number. I'll just note that last night, using my intuition, it was the most likely outcome.
Still, this probability has roughly doubled from a few weeks ago, when the chances had been hovering at about 0.3 percent instead.
Here's what the 12th Amendment says about determining the winner:
The person having the greatest Number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote...