What if there's a tie in the electoral college?

I was pretty well taken with this notion for a good portion of the day yesterday.

I came up with a pretty plausible electoral map that would result in a 269-269 tie between the Democrats and the Republicans.

Here's how it works.

Dems win CA, OR, WA, NM, CO, MN, IA, IL, WI, MI, PA, MD, DE, NJ, NY, DC, CT, MA, RI, VT, ME.

Reps win the rest. It's a 269-269 tie. Draw it on your map, or do it here.

So we know that then the election for president is thrown into the House of Representatives. The VP is chosen by the Senate. The following questions result:
- Does the 110th (current) Congress elect, or the 111th?
Answer: The Constitution, specifically the 12th Amendment, says that "immediately" upon the counting of the electors in Congress, the election in the House is held - so it's the 110th, since electors meet in early December. Which means, of course, that whoever is about to become president will also be voting for his or her vice president!
- Can the Senate filibuster a VP choice? (presumably yes, but this requires more research)
- Does the voting happen concurrently, or does the House vote first, then the Senate? There's no immediate constitutional information about this.

During my research I found out a giant wrinkle. If the election were thrown to the House, each state gets ONE vote, and the new president receives a majority of the states. States presumably caucus as delegations to pick a winner. So theoretically, a Republican could "win" a state in the House election that he "lost" in the electoral college, and vice versa.

I needed to do some research on what the split in delegations. And found this, courtesy of some awesome wikipedian.
27 states have a Democratic majority.
21 states have a Republican majority
2 states are evenly split
So a Democrat is elected, presumably.