The Senate Conservatives Fund has taken an antagonistic stand against McConnell for months, including by running ads demanding that he support the threat of a government shutdown to defund ObamaCare. 

But the new poll is the clearest sign yet that they're likely to spend heavily to defeat the minority leader.

"There's no question that if Kentucky Republicans nominated Matt Bevin it would be a huge victory for the state and for the entire country. Mitch McConnellAddison (Mitch) Mitchell McConnellLawmakers feel pressure on guns Bipartisan group of House lawmakers urge action on Export-Import Bank nominees Curbelo Dem rival lashes out over immigration failure MORE has a liberal record, he's unwilling to stand up to President Obama, and he's so unpopular that he could cost Republicans the seat," SCF Executive Director Matt Hoskins says in a statement.

"The question is whether Matt Bevin can win given how much money he's up against and how dishonest McConnell is. We've done extensive polling and research on this race and there's definitely a pathway to victory for Bevin, but he won't win unless the grassroots rise up," Hoskins said. "That's why we're seeking input from our members in Kentucky and across the country to see if the support is there to win this race."