I'm not too sure a bitter fight completely makes that not possible, Obama may not have had Hillary as his running mate but they certainly cooperated and he gave her the top cabinet position, Bush and Reagan in 1980 got kind of nasty as well. Also Gingrich/Romney was the real nastiness ("When Mitt Romney Came To Town"), though Santorum/Romney is just getting started I suppose.
That's different though. In those cases, Obama and Reagan respectively already had the nomination won. At that point, you might as well be a good soldier. But the scenario we're talking about is one in which the nomination is still contested. Why the heck would either Romney or Santorum just give up, simply because the other candidate has a few more delegates and votes than they do, albeit not a majority? They're not going to give up a real chance at the nomination just for the vice presidency, not after a months-long bitter primary fight, with all of their supporters egging them on to keep going.
The only way it would happen is if one of them becomes convinced that the other guy is sure to win it anyway, even without his cooperation. In which case, time to make a deal. Otherwise, it's a smarter bet that they'd try to woo Gingrich and Paul and their delegates, as well as try to convince delegates from each others' camps to jump ship.