So, here's an oddball scenario. It's highly improbable, yet still possible. So for your entertainment and amusement, let's say that Romney captures four of them, and Obama gets three, and they fall in line just right, with the result that both Romney and Obama each end up with 269 electoral votes. That tosses the election of the president into the House of Representatives.
Now, in the House, each state delegation gets one vote, and it takes 26 votes to win the presidency. So, take Virginia, which has 11 representatives. If six are Republican and five are Democrats, it's quite likely that Virginia will cast its vote for Romney, even if Obama won the state's popular vote by ten points, 55-45.
The election of the vice president goes to the Senate, and just for the sake of argument, let's say the Republicans gain three seats, and there is a 50-50 split. Joe Biden is the constitutionally designated President of the Senate, and has the power to cast the deciding vote in the event of a tie.
All this occurs within a day or two of the new congress being sworn in on January 4. Since inauguration day for the president and vice president is January 20, he's still the President of the Senate, and could still cast the tie breaking vote, even if he votes for himself.
Again, for this to happen, everything has to fall into place just right. But if it does, there is a possibility that we could have a President Romney and a Vice President Biden.
Our Constitution is a marvelous document.

Drawscore