I have turned over too many plausible tie scenarios in the Electoral College (play around here) to neglect looking beyond Election Day to our eminently logical contingency procedures.
Short answer, if you want to skip the next few paragraphs: in case of a tie, Obama wins.
The long answer is that elections not decided in the Electoral College are decided in the House. But members do not vote – states do. This is called the Unit Rule. Each state's delegation to the House meets and casts a single vote. We expect that this takes place along party lines within the states, i.e. Indiana has 5 Democrats and 4 Republicans, and hence Indiana's 1 vote presumably goes to Obama.
The incumbent Congress, not the folks who get elected in November, make the call (see comments for correction: incoming Congress decides). Right now, here is how our state delegations break down:
Republican (21): AL, AK, DE, FL, GA, ID, KY, LA, MI, MO, MT, NE, NV, NM, OH, OK, SC, TX, UT, VA, WY
Democrat (27): AR, CA, CO, CT, HI, IL, IN, IA, ME, MD, MA, MN, MS (!!!), NH, NJ, NY, NC, ND, OR, PA, RI, SD, TN, VT, WA, WV, WI
Split (2): AZ, KS
The scenario, even assuming AZ and KS throw their support to McCain, clearly favors Obama. The GOP, in response, will suddenly develop a very principled stance (unrelated to the fact that standard unit voting leads to their defeat) in favor of state Congressional delegations voting in accordance with the popular vote in their states. This, coincidentally, would almost certainly lead to a McCain win, as the GOP excels at winning lots of states in which no one lives.
Of course the Democrats in the House wouldn't go along with that at gunpoint, but that's not the goal. The goal will simply be to flood the talk radio airwaves with torrents of "fairness" and "disenfranchising" and "the will of the people" talk.
I wouldn't call a tie likely, but it could happen. Among swing states, let's say IA, MN, CO, and NM go to Obama. Give McCain VA, OH, and NH and you've got yourself a tie. That, in my opinon, is entirely plausible. Accordingly I have a hard time seeing how McCain wins without sweeping the big trio of OH-PA-VA. Single-state polling isn't great, but Obama has sizeable leads in IA, NM, MN, and other supposedly competitive states that McCain would have to win if he doesn't sweep the Big Three.
(Polling caveat: I rip on it a lot, but even if results fall within margins of error I subscribe to the belief that consistency counts. For example, Obama's lead in various Michigan polls is always within the margin of error but he is the consistent winner in poll after poll (see also: McCain in Missouri). While I wouldn't put any stock in a single poll showing one guy with a 2-point lead, twelve polls over 4 months are a different story.)