Any person, having been elected to the office of United States senator, shall be forever ineligible to be elected to the office of president of the United States. The purpose of this amendment isn’t so much to protect the presidency, as to protect the Senate. Very few senators ever become president, but of the 100 people serving in the Senate at any given time, probably about 95 think they’ve got a shot. This causes them to treat their Senate service as a potential steppingstone, rather than an end in itself. Ban senators from higher office and you encourage them to focus on their jobs. Plus, a Senate that couldn’t serve as a steppingstone might attract a better caliber of senator.
I dunno. Harry Reid seems to have no further ambition, and he’s about as small-caliber (or large-bore, if you’re thinking shotguns) as they come.
I see one potential sticking-point: the existing senators, at least the 95 who covet the White House, aren’t going to go for this unless it’s written specifically to exclude anyone in office at the time of ratification. (Once a greedy pygmy, always a greedy pygmy.)
The more arguable point, though, is whether this would have more of a salutary effect than simply repealing the 17th Amendment and returning the selection process to the states. Opinions differ on the exact benefits of getting away from direct election of senators, though one of them, at least to me, is never again finding myself in a crowd of people and thinking “Christ, some of these people actually voted for Jim Inhofe.”