Several recent electoral projections have shown a 269-269 split. There are many combinations that are possible that would create this split. One I remember from playing with the electoral calculator is that Florida could go for Kerry but Oregon and Washington could go for Bush. All other states vote as they did in 2000. That's obviously Plausible, all three states were less than 1% in the last election I think. Obviously Florida was a lot less (600 votes out of millions!). I think the chances are low but not lottery ticket low.
The Dems would use fillibuster type dirty tricks. First they would try to break the quorum requirement by having 1/3+1 of 50 states not show up to vote. 33.3 is 2/3 of 50. Already we see grounds for Democratic legalistic arguments.
Also how does a "split state" decide to cast it's vote. Even the simple expedient of simple majority is not called. Obviously some Lani Grannier types will suggest proportional voting, or caucus based voting, or 2/3 majority of the state.
So say it is 34 to win. That means if the Dems control 17 states they can prevent the quorum and therefore the election in the house. One only has to look at their behaviour vis-a-vis the Supreme Court to KNOW they would try it.