The veep-stakes are heating up. The press is churning out articles touting various vice-presidential contenders, and there has already been one wave of public polling as buzzy favorites like Louisiana Gov. Bobby Jindal and Ohio Sen. Rob Portman get plugged as favorites.

Despite the hype, presidential candidates often end up choosing running mates who weren't even on the radar. No one could have predicted the selection of Dick Cheney in 2000, let alone that of Sarah Palin in 2008. Here are some of the contenders that so far have been ignored by “the Great Mentioner” in the Republican race for vice president.

John Barrasso
John Barrasso is a relatively obscure first-term senator from Wyoming, a deep-red state of fantastically little electoral significance. He does bring two assets to a Republican ticket, however: Barrasso is a Catholic and a doctor. One of the fall campaign's big issues will no doubt be the Affordable Care Act, and on this, Barrasso would be the perfect surrogate for the Romney campaign. He was a steadfast opponent of Obamacare in the Senate and thus is not tainted, like Romney, with past support for a mandate. Barrasso is not an unblemished conservative though. Like Romney, he was pro-choice early in his political career before moving to the right on social issues along with the Republican base. Then again, George W. Bush was pro-choice at one point, too, and that didn’t hurt him with social conservatives.

Terry Branstad
Branstad, the five-term governor of Iowa, is the rare running mate whose presence on the ticket could almost certainly deliver a swing state. The problem is that that swing state is Iowa, with a mere six electoral votes. One prominent Democratic operative in Iowa said that Branstad would be worth several percentage points there—likely enough to swing the perennially purple Hawkeye State. There are reasons Branstad hasn’t been mentioned, though. He’s 65 years old and not very charismatic—his trademark mustache seems to have inspired Will Ferrell’s facial hair in Anchorman. Branstad also hasn't been known as a social conservative and won’t help Romney with that key GOP demographic. And although he has never served on Capitol Hill, he doesn’t exactly add to the outsider image that Romney is trying to cultivate. He has served five terms as governor of Iowa (four from 1983 to 1999, and he was elected to his fifth in 2010.) For all these flaws, Branstad would deliver a state that’s up for grabs, which is more than most potential GOP running mates could do.

Sam Brownback
Romney may be feeling pressure to choose a devoutly Catholic social conservative with a strong legislative record in the Senate, but Rick Santorum is problematic for obvious reasons. Instead, Sam Brownback, the governor of Kansas, fits all of those qualifications without the downside of having said lots of nasty things about Romney recently. Unlike Santorum, however, Brownback is not from a swing state and thus doesn’t provide any direct electoral value. But if Romney feels the need to choose a staunch social conservative, Brownback may be his best bet.

Eric Cantor
Eric Cantor, the House majority leader with impeccable conservative credentials, would help Romney with certain swing voters—but not necessarily in his home state of Virginia, where he represents a gerrymandered district that cuts a diagonal gash across the state. Instead, Cantor would represent the culmination of a longtime Republican effort to woo Jewish voters away from the Democratic Party. Although Jews make up only about 2 percent of the U.S. population, they have disproportionately high turnout rates and are heavily concentrated in key swing states like Florida and Ohio. Cantor, though, has already claimed no interest in being Romney’s running mate. If selected, he would have to give up his seat in the House and any hope of supplanting John Boehner as speaker. Further, a ticket made up of a Mormon and Jew might not sit too well with conservative evangelicals.

Judd Gregg
This former New Hampshire senator would not provide geographic or ideological balance to the ticket—Gregg occupies roughly the same center-right point of the political spectrum that Romney does. But Gregg’s selection would reinforce the image that Romney is trying to convey to swing voters as a pragmatic fiscal conservative. It would also solidify Romney’s standing in the swing state of New Hampshire. There are downsides, as well. A ticket consisting of “a Massachusetts moderate” and “a New Hampshire moderate” is not what social conservatives are looking for and may just seem too East Coast for many voters in the Midwest and Mountain West. (Not to mention, Gregg’s hometown of Nashua literally touches the Massachusetts state line.) Gregg will also face scrutiny over his ties to the Obama administration—in 2009 he accepted an offer to be Obama’s secretary of commerce before changing his mind. The advantage of choosing Gregg is that he reinforces Romney’s strengths. The problem is he does nothing for Romney’s weaknesses.

Joe Scarborough
Another wild card would be Joe Scarborough, the voluble morning-talk-show host on MSNBC. Prior to becoming a television personality, Scarborough was a very conservative congressman from west Florida for six and a half years. In contrast to his voting record, Scarborough has a moderate image because of his stint on MSNBC. It’s not terribly likely that Romney will pick Scarborough. And he hasn’t served in elected office since before Sept. 11, 2001. Then again, Scarborough is a telegenic, articulate candidate with strong conservative credentials from a swing state. Romney could do worse.