The Republican-leaning group American Crossroads is assailing Judd in its own online video that also plays up the fact that she lives in Tennessee, and that she campaigned for President Barack Obama, who is unpopular in Kentucky.
Kentucky House Republican Leader Jeff Hoover said getting Judd into the race would be a boon for the state GOP because of her liberal views.
"I hope she does enter the race," Hoover said. "I think if she becomes a candidate for U.S. Senate, it will almost guarantee that we will become the majority party in the Kentucky House. Her statements on coal, her statements on traditional values are way outside what every day, hardworking Kentuckians think."
Hoover said Judd has proven a distraction for the Legislature.
"We can't seem to get pension reform done or any of the other things we need to get done because House Democratic leadership is too concerned about who has talked to Ashley, who didn't talk to her, and who she called or didn't call," Hoover said. "I just think we need to get past someone who lives in Tennessee and focus on Kentucky problems."
Beshear said his last conversation with Judd was via telephone.
"I would say without getting into the specifics of the conversation that I'm convinced she is seriously considering a race for the U.S. Senate," he said. "And we'll see where it goes."
Conway said he believes any well-known Democrat who can raise money and can articulate a positive vision for Kentucky can beat McConnell.
"He's vulnerable because he's become the poster boy for the gridlock in Washington," Conway said.
House Speaker Greg Stumbo said the outcry from Republicans about Judd entering the race is telling.
"They're scared," he said.