BOWLING GREEN, Ky. — Memo from home to Senator Rand Paul: Be careful what you wish for.

Back when Mr. Paul, the curly-haired libertarian darling with the snappy fashion sense, was still a hot presidential prospect, he hatched a plan to skirt a state law barring candidates from being on two ballots at once. If Kentucky Republicans staged a caucus — à la Iowa — to pick their presidential nominee, Mr. Paul could seek the party’s nomination for the White House and re-election to the Senate, too.

“It doesn’t really pass the smell test, running for two offices at once,” said Jim Skaggs, a longtime Republican official and neighbor of Mr. Paul here, describing the initial reaction from the party establishment, which acquiesced in the end. “It was very skeptical, to say the least.”

Now, Mr. Paul’s presidential campaign is in the tank, with poll numbers so dismal that he was kicked off the main stage of the Republican presidential debate last week in North Charleston, S.C. But even if Mr. Paul dropped his presidential bid, his name would remain on the ballot in the Kentucky caucus March 5. Some in the state say he risks losing a contest that he himself engineered — a development that could prove embarrassing in his other race, the one for the Senate.

“There’s a lot of folks that don’t see him as necessarily the first choice right now,” said Scott Lasley, the chairman of the Warren County Republican Party here in Mr. Paul’s hometown, Bowling Green. Asked if he backed Mr. Paul, Mr. Lasley, a political scientist at Western Kentucky University, replied: “Ummm? Off the record?”