The best chance for Romney, Gore, and Paul, possibly:
Dark Blue-Paul-240
Dark Red-Obama-111
Light Red-Hillary-86
Light Green-Gore-55
Gray-Romney-46
While if you stack up all three Democrats against Paul, they win a plurality by sixteen points, if Romney and Paul go together, they win.
The election goes to the House where Paul, Obama, and Hillary fight it out. A small number of Republicans defect to Hillary because of Paul's "extremism", however, Paul wins and America, after only four years ago electing its first African American President, gets its first Hispanic Vice-President.