It could happen. If Obama and Romney each get an equal number of electoral votes, the election is then decided by the newly-elected Congress. The House will pick the President, and the Senate gets to pick the Vice-President. I bet you can see how this is going already.
Even after the election, it's most likely that the Republican-controlled House will go for Romney. Similarly, it's most likely the Democrat-controlled Senate would pick Biden. Voila! The political odd couple, Romney-Biden.
It's also entirely possible that the Senate would wind up split right down the middle after the election -- 50 Democrats and 50 Republicans. In that case, an even odder situation ensues. The new Vice-President would be selected by the sitting Vice-President. Who do YOU think Joe Biden would vote for? (Source: ABC News, A Romney-Biden Administration, October 22, 2012)
What This Means for You
In this unlikely scenario, life would pretty much operate as it would under a Romney-Ryan win. That's because the Senate would be split down the middle, a more conservative situation than exists now. Despite being Vice-President, Biden would probably not get much face time, or influence, in the new administration. Therefore, Romney's economic policies would probably be carried out as detailed in his Economic Plan.