Washington CNN —  

Republicans on Capitol Hill weighed in on news that Mitt Romney might be exploring a possible third bid for the White House, but it was Arizona Sen. John McCain who might have drawn the most laughs of the day in talking about the potential presidential aspirations of his best friend Sen. Lindsey Graham.

McCain said Romney was dedicated to serving the country and was a fine and decent American with a reservoir of support and called himself “a great admirer of Mitt Romney’s”, but he said he was pushing Graham to run.

“My illegitimate son Lindsey Graham is exploring that option,” the two-time presidential candidate said, prompting laughter from reporters during a press conference on the prison at Guantanamo Bay.

“So I am strongly encouraging Sen. Lindsey Graham, particularly with the world the way it is today. No one understands the world today in the way that Lindsey Graham does, in my view.”

Romney recently met with prospective donors, has spent time talking with former operatives and supporters and is planning a trip to the upcoming Republican National Committee meeting in California this week, signs that he could decide to enter the fray for a third time.

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Asked whether it made sense for voters to give the former Massachusetts governor a third look, McCain said he didn’t know, but added that Romney would be a “viable” candidate should he run.

Meanwhile, New Hampshire Sen. Kelly Ayotte dodged questions about whether she would support a third Romney run, saying she looked forward to speaking with all the candidates in what was sure to be “a very vigorous field”.

Earlier, House Speaker John Boehner dodged questions about Romney. “Well, I’ll let him make that decision,” he said at his weekly press conference. “We’ll see a lot of candidates making announcements in the coming months I expect, so it’s a very open process. May the best person win.”