Reince Priebus, the Republican National Committee chairman, was asked on NBC's "Meet the Press" about Republican strategist Karl Rove's reported comments that Clinton might have suffered brain damage from a 2012 blood clot. Priebus refused to distance himself from Rove's remarks or say he should apologize.
"I think that health and age is fair game," Priebus said. "It was fair game for Ronald Reagan. It was fair game for John McCain."
Reagan took office in 1981 at age 69; McCain, the Republican candidate in 2008, was 72 on Election Day that year.
The New York Post reported that Rove made the suggestion at a recent conference. Rove denied using the phrase, but told Fox News Clinton's health would be an issue should she run.
Clinton suffered a blood clot in her head in December 2012 after falling at her home and received several days of treatment at a New York hospital. The incident raised health concerns for Clinton, who was a widely traveled secretary of state during President Barack Obama's first term.
Her husband, former President Bill Clinton, said last week, "There was nothing to it ... She is strong. She is doing great.
Former New York City Mayor Michael Bloomberg blasted Rove's comments as beyond the pale. "I thought his remarks just were outrageous," he said on CBS's "Face the Nation" on Sunday.
Bloomberg called Clinton a "great American" who would make a "spectacular candidate on the Democratic side."
"You can't ask somebody to do more than she has done for her country," said Bloomberg, a long-time Democrat who switched to the Republican Party when he first ran for mayor. He later dropped his party affiliation altogether.
Democrats accuse Republicans of politicizing the blood clot as part of a strategy to discourage Clinton from running.
"They do not want Hillary Clinton," Senator Claire McCaskill told NBC. "Because they know she is going to ignite a spark of enthusiasm across this country and she has got the strongest resume for president of anyone who's run in a very long time."
She called Rove's reported comments, which also drew a swipe last week from White House spokesman Jay Carney, "a cheap political shot."