Former Florida Gov. Jeb Bush, left, listens as President Obama speaks during a tour of Miami Central Senior High School earlier this month. (AP Photo/Pablo Martinez Monsivais) (Pablo Martinez Monsivais/AP)

At this point, though,we have a good sense of how the field will shake out – or at least who might run. Former Massachusetts governor Mitt Romney, former House speaker Newt Gingrich, former Minnesota governor Tim Pawlenty and former Pennsylvania senator Rick Santorum are basically in, while several others – former Alaska governor Sarah Palin, former Arkansas governor Mike Huckabee, Indiana Gov. Mitch Daniels – are giving it serious thought.

But there’s (almost) always a surprise entrant in presidential races — particularly one as wide open as 2012 appears to be. Former Sen. Fred Thompson (R-Tenn.) was hailed as a game-changer when he entered the 2008 election late. (That didn’t pan out). Few thought Sen. Barack Obama (D-Ill.) would run (until he did).

There have already been a few surprises this time around. Almost no one was talking about Jon Huntsman as a 2012 candidate from the time he was appointed Obama’s Ambassador to China until, well, it became clear that he is likely to run.

So while we have our preconceptions about who will run, it’s always subject to change. Candidates will rule out a run one month and then open the door the next (See: Daniels, Mitch).

With that in mind, who on the Republican side could really throw a wrench into the calculus of the 2012 presidential election if he (or she) decided to run? Who are we not talking about who could really make an impact?

After the jump, we analyze a few off-the-radar candidates who would have an instant effect on the race in the unlikely even that they do run. (A caveat: history is not quite so littered with these candidates actually winning. And most of these people have unequivocally ruled out running for president. We don’t expect any of them to run. All we’re saying is, ‘If they did for some reason, then x-y-z.’)

Former Florida governor Jeb Bush

Few Republicans get such universal praise from fellow GOPers as Bush, the younger brother of the former president. And almost everyone acknowledges that if George W. Bush hadn’t left office on such poor terms, we might be talking about Jeb for president right now. Despite the former Florida governor showing no interest in running, National Review Editor Rich Lowry put Jeb on his magazine’s cover last month and is publicly urging him to run. Bush could pretty easily win votes from both the establishment and tea party crowds, though his relatively moderate views on illegal immigration may be a major liability. Either way, though, he would instantly be a major factor.

New Jersey Gov. Chris Christie

Almost nobody has said “no” to a presidential bid in so many ways – he even suggested suicide would not put the rumors to rest – and almost nobody who has ruled it out continues to get as much attention as Christie. That’s because that New Jersey governor seems only too happy to continue building a national profile just more than one year into office. With tough-talking, crusading GOP governors now in vogue, Christie could stake claim to being the truest fiscal conservative in the bunch. If the GOP continues to push for big budget cuts, Christie may be best-equipped to carry that banner.

Gen. David Petraeus

Americans aren’t terribly fond of the mission in Afghanistan anymore, but Petraeus gets rave reviews from nearly everyone. A Gallup poll from July 2010 showed him with a 56 percent favorable rating, with just 9 percent viewing him unfavorably. That puts him on better footing than any other potential GOP presidential candidate. Now, in fairness, he would have to learn how to be a politician, and running as a general when all the top issues are based on the economy is not ideal. But with a GOP field that some see as lackluster, Petraeus could bring something totally different to the race.

Sen. Jim DeMint (R-S.C.)

The second-term GOP senator, in addition to emerging as a kingmaker for tea party candidates in Republican primaries in 2010, has recently shown that he also has significant fundraising prowess. If other tea party candidates don’t run (a distinct possibility) or fizzle early (also a possibility), DeMint could immediately jump in and fill that void. Many Republicans are surprised that DeMint isn’t more actively considering a run, and almost everyone recognizes that he would be a force — especially in his home state of South Carolina.

Texas Gov. Rick Perry

The timing seems a little too perfect for Perry. After not cultivating much of a national profile for his first 10 years as governor, he’s been jetting around the country and earning strong reviews from the tea party base. The governor came away stronger than ever after a primary challenge from Sen. Kay Bailey Hutchison a year ago . He’s saying all the right things to appeal to the right and – apart from being a little too George W. Bush-y – has the kind of heavyweight profile that would be instantly competitive. But, he’s the chairman of the Republican Governors Association, a commitment that suggests he stays out.

New York City Mayor Michael Bloomberg

Bloomberg may be increasingly unpopular in his city. But it’s hard not to think he and his billions of dollars could swing a presidential election if he decided to run as an independent. Even though polling has suggested he would stand little chance of winning the race, he would could well be a Ross Perot-like figure, giving dissatisfied voters another option. Whether that hurts Republicans or Democrats is an open question, but Bloomberg wields significant power if he ever did decide to run.

Marco Scott Paul

We have combined GOP Sens. Marco Rubio (Fla.), Scott Brown (Mass.) and Rand Paul (Ky.) for the simple reason that it would be highly unusual for a brand-new senator to run for president (even Obama waited until he had been in the Senate for two full years). All three men were elected with strong tea party support, but mostly, they would bring young, fresh perspectives to what is otherwise a relatively conventional field. Imagine Paul, rather than his father, Rep. Ron Paul (Texas), jousting with fellow Republicans on budget cuts. Or Rubio telling his life story standing alongside Romney.

Sen. Rob Portman (R-Ohio)

Portman suffers from the same thing as the three senators mentioned above; he was just elected in 2010. But if you ask smart Republicans who of the 47 GOP senators is made of presidential timber, Portman’s name quickly rises to the top. He has cultivated an expertise on fiscal issues as a former director of the Office and Management and Budget, is personally affable and is a quality campaigner – the kind of established politician who just seems like a presidential candidate, be it in this election or one down the road.

Rep. Paul Ryan (R-Wis.)

The House Budget Committee chairman’s name comes up from time to time, mostly as the GOP looks to future presidential elections. It’s hard to see him thinking he has much of a shot at winning a presidential race coming from the House — the last person to do that was James Garfield way back in the 19th century -- but as far as respected voices of fiscal conservatism in Congress, Ryan is your man. He could enunciate economic arguments in ways that many other GOP presidential candidates can’t and has been willing to go further than his colleagues on issues like Social Security cuts. That means something to the tea party base.

Former DNC Chairman Howard Dean

Obama seems to have mollified the liberal base after a series of events led to some wondering if he would get a primary challenge in 2012. His administration’s moves to placate the left on things like “Don’t Ask, Don’t Tell”and the Defense of Marriage Act have worked. But Obama will continue to have to work with a Republican-led House, and a compromise on spending cuts or other issues could compromise that detente.