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Donald Trump is keeping the door open to a possible presidential bid, stoking rumors again today that he could toss his hat into the ring and run as an independent if he does not believe the eventual Republican nominee can beat President Obama.

"It's not something I want to do, but if I don't see a person that, number one, is going to win I would certainly think about doing it after the show ends," Trump said on CBS' "Face the Nation," referring to his reality TV show "The Apprentice," which ends in May.

Trump said he is considering endorsing one of the current GOP candidates. If the man he endorses wins the nomination, Trump said he "absolutely would not run."

But the millionaire real estate mogul said the Republican candidates are "hurting themselves" and their chances of beating Obama because the "level of hatred" in the primary race is so high.

Obama advisor David Axelrod agreed, telling NBC's David Gregory that the primary process "isn't helping" Mitt Romney, in particular, and that as a result the primary race "will go on for a while."

"I still think he is a weak frontrunner," Axelrod said on "Meet the Press." "He overpowered [Newt] Gingrich in Florida with a spending advantage and very negative campaign. He's still under water nationally."

But former GOP candidate Michele Bachmann said the often scathing back-and-forth between frontrunners was just "the normal rough and tumble of a campaign."

"This is normal," Bachmann said on "Face the Nation."

Republican National Committee Chairman Reince Priebus agreed, saying "tough" primaries such as this serve to make the eventual nominee "tougher and battle tested."

"History shows tough primaries and a little drama are good for the challenging party," Priebus said on "Face the Nation." "I think it's good for America. And in a few months this is all going to be ancient history."

Responding to fresh attacks from Gingrich, who said today on ABC's "This Week" that Romney's character was a "very serious problem," Priebus defended the former Massachusetts governor as a "man of integrity."

"I think all of our candidates are men of integrity," Priebus said. "Primaries are tough. In the end our party is going to come together and we are going to get serious about beating Barack Obama."

Shifting the focus to the president, Priebus compared Obama to Italian cruise ship Capt. Francesco Schettino, who allegedly fled the Costa Concordia after it ran ashore and partially sank earlier this month.

"We're going to talk about our own little Captain Schettino, which is President Obama who's abandoning the ship here in the United States and is more interested in campaigning than doing his job as president," Priebus said.