With Mitt Romney all but assured of winning the Republican presidential nomination, speculation is growing about his choice for a running mate.

On “Fox News Sunday,” former Arkansas governor and 2008 Republican presidential contender Mike Huckabee said Florida Sen. Marco Rubio should be on the GOP ticket.

“That would be my choice. And he shouldn’t do it early because that just gives people more time to go after the target. … You can put all the potential VP people out on the campaign trail, but as soon as you name somebody, all those other ones, they’re off the trail,” he said.

The former Arkansas governor, who has been mentioned himself lately as a vice-presidential pick - evangelical leader Richard Land last week was the latest to talk up a Romney-Huckabee ticket - downplayed those reports.

“I haven’t gotten a call and I doubt I will, so I just merrily go about doing my business,” Mr. Huckabee said Sunday. “I think his better pick is Marco Rubio.”

Other Republicans are skeptical about the Florida senator.

Alberto Gonzales, the attorney general in the George W. Bush administration, said Saturday on CNN that Mr. Rubio’s “resume does not reflect someone prepared to confront serious and dangerous issues that our country faces as president.”

Ed Gillespie, a former Republican National Committee chairman who recently joined Mr. Romney’s campaign as a senior adviser, said Sunday that he has no idea whether the campaign is considering naming a vice-presidential candidate well before the party convention in August, as some have suggested.

“The fact is, the Romney campaign and Gov. Romney himself really only emerged as what I think is now safe to say the presumptive nominee for the Republican Party about a week ago,” Mr. Gillespie said on “Fox News Sunday.” “So the focus had been rightly on trying to secure enough delegates to win the primary.”

He also dispelled recent reports that the campaign has selected him to head up the vice-presidential search committee.

“I saw that report,” Mr. Gillespie told host Chris Wallace. “It was news to me and as far as I know it’s not accurate.”

Mr. Romney has remained tight-lipped about whom he might select, though speculation often centers on Mr. Rubio, New Jersey Gov. Chris Christie and Virginia Gov. Bob McDonnell.

Other Republicans have been quick to weigh in.

Sarah Palin and former GOP candidate Herman Cain have said Mr. Romney should pick Florida Rep. Allen West, a tea party favorite and the only Republican member of the Congressional Black Caucus.

Republican National Committee Chairman Reince Priebus said Sunday that the party hasn’t officially declared Mr. Romney the nominee “out of respect” to Ron Paul and Newt Gingrich, who are still running but lag far behind in delegates. But Mr. Priebus admitted on CNN’s “State of the Union” that he knows the race is virtually over.

“You haven’t officially declared it, but you’re kind of out there thinking it?” anchor Candy Crowley asked.

“Well, sure,” Mr. Priebus said.

“I mean, Mitt Romney had a great month and he’s clearly on a pathway to be the presumptive nominee and we’re going to have a unified party when this is all said and done,” he added. “And the reason we’re going to have a unified party is that, no matter where you fit in - Republican, conservative, independent - this is not, Candy, about the future of the Republican Party. … This election is about the future of America.”

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