“I say we place in peril our control of the State Legislature,” said Dale Emmons, a strategist who advised the last unsuccessful Democratic challenger to Mr. McConnell, in 2008.

He added, “Her Siamese twin will immediately be Barack Obama,” who lost Kentucky by 23 percentage points in November.

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.”