Sen. Mitch McConnellAddison (Mitch) Mitchell McConnellAlabama election has GOP racing against the clock McConnell PAC demands Moore return its money Klobuchar taking over Franken's sexual assault bill MORE (R-Ky.) says he will back his primary challenger, businessman Matt Bevin, if Bevin nabs the nomination this month.

But that pledge likely won’t be necessary come May 20, as Bevin’s campaign has stalled over the past month and looks unlikely to come out on top. Bevin's campaign, however, has not yet said whether the candidate will commit the same support to McConnell.

According to the Lexington Herald-Leader, the Kentucky GOP is asking the candidates to sign a pledge committing to support the eventual party nominee.

"We stand united to help ensure GOP unity for the general election next November," the pledge reads. "We pledge our full endorsement and support to the Republican nominee for U.S. Senate immediately following the declaration of a winner in the primary election on the night of May 20, 2014."

McConnell spokeswoman Allison Moore told the Herald-Leader that "from day one, Sen. McConnell has committed to supporting the winner of the primary election."

"The stakes of this election are too high to give President Obama another vote in the U.S. Senate with Alison Lundergan Grimes," she said.

Bevin’s campaign did not respond to a request for comment.

While McConnell is favored in the primary, he's facing a much tougher fight against Democrat Alison Lundergan Grimes in the general.