Portman could easily run for reelection while pursuing the Vice Presidency, not sure about New Hampshire or South Dakota election laws regarding running for two offices at once. If there is a prohibition against seeking two offices at once, then I can't conceive of either Ayotte or Thune running.
It's not about the legality of the matter. It's the practical matter of running in a competitive swing state for two offices at once, letting everyone know that the Senate seat is your "fallback" choice, and spending very little to no time doing any actual campaigning for the Senate race. Sure, it works if you're really popular in the state, or if the state is heavily tilted toward your party (a la Connecticut in 2000 with Lieberman). But it wouldn't work for Ayotte or Portman in 2016.
