Another Kentucky-based consultant, James Cauley, said he began hearing fears from Kentucky officials last month when Ms. Judd attended the Bluegrass Ball in Washington during the inauguration, where she confirmed she was “taking a close look” at a run.

“People started saying, ‘Oh my God, she is serious,’ ” said Mr. Cauley, who managed Mr. Obama’s 2004 Senate campaign in Illinois. “One state legislator asked me to go to the White House and talk to Barack.”

Mr. Cauley demurred. He and the president are not close.

Ms. Judd, 44, who has starred in “Ruby in Paradise,” “Double Jeopardy” and other movies, spent much of her childhood here in Ashland, in the Rust Belt of eastern Kentucky. Her mother is the country singer Naomi Judd, and Wynonna Judd, another country star, is a half-sister.

She attended the University of Kentucky and regularly returns for home basketball games in Lexington, sometimes leading the crowd in cheers for the Wildcats.

But her primary residence is outside Nashville. She was a Tennessee delegate to the 2012 Democratic National Convention, speaking on behalf of President Obama. She has been outspoken for animal rights and against violence toward women in Africa. More relevant to Kentucky, perhaps, is her opposition to mountaintop-removal coal mining, which many oppose but which no prominent candidate has publicly denounced for fear of losing support in coal country.

Mr. Yarmuth, who is the only Democrat in the state’s Congressional delegation, dismissed concerns that Ms. Judd would be a liability. On the contrary, he said, she would neutralize Mr. McConnell’s fund-raising advantage and energize opposition.