In a sometimes testy televised debate Monday night, Paul's chief Republican opponent, Kentucky Secretary of State Trey Grayson, said he "proudly" would vote for McConnell. McConnell has endorsed Grayson in the May 18 primary.
The debate is the final face-off in what has become an increasingly acrimonious race to replace Sen. Jim Bunning.
Paul, a Bowling Green eye surgeon with strong backing from tea party activists, has been engaged in a bitter race Grayson. Paul is leading in the polls.
The eventual Republican nominee will face one of five Democratic candidates, including Lt. Gov. Daniel Mongiardo and Attorney General Jack Conway.