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Some men are at least trying to be that unifying figure. And by the way, they are all men. At CPAC on Saturday, there will be a presidential straw poll featuring some of the people who may run for president in 2016.
NPR's Mara Liasson reports on the possible GOP field.
MARA LIASSON, BYLINE: Yes, it's four years away, but that hasn't stopped Republican hopefuls from testing the waters. There are already polls, for whatever they're worth, of potential GOP candidates. One name that's usually at the top of the list, says political analyst Stu Rothenberg, is the CPAC reject Chris Christie.
STU ROTHENBERG: Christie has gotten wonderful general-election ink over the last six months - somebody who's a straight-talker, not the photogenic, artificial, phony politician. And he's benefited in his overall profile from a positive relationship with the president and his willingness to take on his own party.
LIASSON: Having said that, Rothenberg adds, those are exactly the attributes that will hurt Christie with Republican primary voters if he seeks the nomination.
Christie is asked about running all the time. And he's adopted a: what are you nuts? response.
GOVERNOR CHRIS CHRISTIE: I think anybody who tries to plan in politics that far in advance is crazy.
ROTHENBERG: Bobby Jindal takes the same approach.
GOVERNOR BOBBY JINDAL: Anybody on the Republican side even thinking or talking about running for president in 2016, I've said, needs to get their head examined.
LIASSON: Jindal is the Indian-American governor of Louisiana - he's widely considered to be mulling a run and he's joked about the unlikely chance that a skinny, brown guy with a funny name could become president.
But not every Republican thinking about 2016 is so coy. Kentucky Senator Rand Paul is the libertarian Republican who shot to prominence last week with an old-fashioned, 13-hour live filibuster against the administration's killer drone program.
SENATOR RAND PAUL: In order to grow and win national elections again, we're going to have to have somebody a little bit different than we've had in the past, someone who has a little bit more of a libertarian Republican approach.
LIASSON: Stu Rothenberg says Paul has established himself as a force to contend with inside the GOP.
ROTHENBERG: I think Rand Paul is the leader of the Tea Party wing of the party, because he can get people to vote; he can also get them to turn out in caucuses.
LIASSON: There is one Republican who many in the party talk about as the adult in the room, the natural front-runner if he were to get in the race - and that is former Florida Governor Jeb Bush, son and brother of former presidents Bush. He will give the dinner address Friday at CPAC, and he was on every Sunday talk show last weekend promoting his new book on immigration. Bush stuck to this standard formula when asked about his plans.
JEB BUSH: Well, I'm not saying yes. I'm just not saying no.
LIASSON: Bush has a ready financial base in his home state, and Florida is the single most important swing state for Republicans. He has impeccable conservative credentials, and he speaks fluent Spanish. Yet one potential rival, Wisconsin Governor Scott Walker, notes what could be Jeb Bush's biggest obstacle - the political baggage of his last name.
GOVERNOR SCOTT WALKER: If you took your finger and covered his last name and just talked about Jeb, there'd be a lot of us who would've been talking about him running for president going forward.
LIASSON: Then there's Florida Senator Marco Rubio - a protege of Jeb Bush who Time magazine recently put on its cover with the headline: "The Republican Savior." But it's hard to see how Rubio runs if Jeb Bush decides to get in.
Some faces from 2012 are likely to return - such as Texas Governor Rick Perry and House budget chair Paul Ryan. Then there's Rick Santorum, the Republican runner-up in 2012. There's also Virginia Governor Bob McDonnell, who was also not invited to speak at CPAC - and right now he is the only potential candidate with an attack ad running against him in Iowa already.
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UNIDENTIFIED WOMAN: Sometime soon, Virginia Governor Bob McDonnell may be in Iowa to test the waters for 2016. But don't be fooled. As a candidate, McDonnell promised Virginians he would never raise taxes. But as governor, McDonnell pushed the largest tax increase in Virginia history on retail, gasoline, property, cars, land, and more. So if Bob McDonnell comes to Iowa, remember: you can't believe a word he says.
LIASSON: 2016 is an open race, with no incumbent running and no Republican in the White House to defend, so it may be the best time since 2000 for a new face of the party to emerge - and the best there will be until after 2020. That's why a whole generation of Republican candidates can be expected to try their luck this time around.
Mara Liasson, NPR News, the White House.