Let's look at the VP first.  In case of an electoral college tie or non-majority, a simple majority vote is taken by the Senate to choose a vice-president; a 50-50 tie would be broken by the VP.

But here's the catch: there is no deadline for the House to choose a president.  Let's say it's a Kerry-Edwards ticket and there's a non-majority in the electoral college and the House.  The Senate goes GOP, or it goes 50-50 and Cheney breaks the tie by voting for himself.  If the House doesn't resolve its own tie for president by inauguration on January 20th, we look to the 20th amendment, which says that the current vice-president "shall act as President until a President shall have qualified."  Vice President Cheney would act as President until the House comes to a resolution.  That can happen at any time during that presidential term of office.  The final kicker: there's no rule that the president and VP have to be of the same party.  So, if the tie in the House breaks for Kerry, we could have a Kerry presidency and a Cheney vice-presidency.

Now wouldn't that be fun? =D