When asked during an interview on CNN's "State of the Union" how he felt about the tightening Florida GOP primary, in which he has already endorsed Crist, McConnell did not signal support for either Crist or state House Speaker Marco RubioMarco Antonio RubioOvernight Cybersecurity: What we learned from Carter Page's House Intel testimony | House to mark up foreign intel reform law | FBI can't access Texas shooter's phone | Sessions to testify at hearing amid Russia scrutiny Cornyn: Senate GOP tax plan to be released Thursday This week: GOP seeks to advance tax overhaul MORE by name.

"I think we're going to elect a Republican senator in Florida, and the Republican voters in Florida are going to determine who that is," McConnell merely said.

"I'm going to be there behind the Republican nominee, whoever that is," he later repeated.

Crist has long trailed Rubio in preliminary polls, and that deficit has only expanded in recent months. The numbers have thus led some to predict Crist might instead run as an independent, though the governor himself has mostly equivocated on that question.

"I'm not thinking about that today,'' Crist told reporters this week. "We'll look at that later on."

But McConnell signaled clearly that Crist would not have much support if he sought his state's Senate seat as an independent.

"He would lose all Republican support if he were to run as an independent," McConnell stated clearly.