Overall, McConnell gets the unconditional backing of only 17 percent of voters, while twice as many, 34 percent, say they'll be voting against him no matter what. A plurality, 44 percent, say they'll have to see who jumps in the race before they decide.

The poll indicates, as a number of other recent polls have, that there may be an opening for a challenger to topple the Senate minority leader despite his long tenure and formidable fundraising capabilities. He currently has nearly $8 million in his campaign account and is already participating in fundraisers and launching robocalls in the state touting his record.

McConnell's campaign spokesman, Jesse Benton, questioned the validity of the poll in an email to The Hill.

"Anyone with a kindergarten level of education in polling knows that asking voters to support an incumbent 'no matter who runs against him' is guaranteed to produce the most skewed number possible. This poll is nothing more than an irresponsible way to stir up cheap headlines," he wrote.

But a poll conducted in December by a Democratic firm showed McConnell with less than 50 percent support when pitted against every potential Democratic challenger, indicating the correct challenger has an opportunity to close his lead. Tea Party groups in the state, too, are hoping to post a challenger against McConnell in the primary, frustrated at what they see as his tacit approval of reckless spending in Washington and bloated federal budgets.

The Courier-Journal Bluegrass poll was conducted by SurveyUSA among 609 registered voters and has a margin of error of plus or minus 4.1 percentage points.

— Updated at 2:39 p.m. to reflect comment from McConnell's campaign