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Joe Gershtenson, a history professor at Eastern Kentucky University and longtime commentator on state politics, said Mr. Grayson’s tenure as the secretary of state could help on Tuesday - but it may be too little, too late.

“He knows all the county judges; he knows the local party officials,” Mr. Gershtenson said. “But this lead that Paul has held has been remarkably consistent over the last two months.”

Mr. Grayson didn’t return requests for an interview, but on Monday night he criticized the anti-Washington, anti-earmarks campaign of his opponent as shortsighted for the state.

Mr. Gershtenson said Mr. Paul’s rise to prominence in Kentucky politics - this is his first bid for public office - was helped by the Bowling Green eye surgeon’s famous father, a maverick GOP congressman who sought the presidency in 2008.

“It would not have been possible if there had not been a Ron Paul,” he said.

The younger Mr. Paul acknowledged a debt to his father.

“Obviously, we’ve benefited from the connection,” he said. “I grew up knocking on doors for him, campaigning for him. We’re both big believers in limited government.”