Darrell Issa
The Democrats and the media would have a field day with the House Oversight and Government Reform Committee chairman, guaranteed. But one of the things that endears this California congressman to the base is that he just doesn’t care who attacks him. In fact, he wears it as a badge of honor. And he goes after everything from stimulus waste to Attorney General Eric Holder and Operation Fast and Furious with gusto and savvy, endearing himself to those Americans frustrated with politicians who don’t get anything done in Washington. Actually, an Issa-Biden face-off could be the best debate ever. But Issa is so no-holds-barred that it would likely prove to be a combustible combination with cautious Romney.

Rod Paige
Bush 43′s former education secretary is already on Romney’s panel of education advisers. He’s not so much a politician as an educator who rose from classroom teacher to be the first African-American to serve as the country’s schools chief. His background has something for everyone: he’s a Navy vet, former head football coach at Jackson State University and Texas Southern University, and an accomplished superintendent who closed in on the achievement gap plaguing urban areas (he calls closing the black-white gap in school achievement “the greatest civil rights issue of our time”). Plus, he once referred to the NEA as a “terrorist organization,” which is pure catnip to the base.

Judd Gregg
The former New Hampshire senator — and chairman of the Senate Budget Committee — has resurfaced on the Hill lately as a deficit ninja of sorts, counseling Republicans through the tricky talks of cuts and revenue. Gregg would be more of a candidate for moderates than conservatives, as he was on the Simpson-Bowles deficit-reduction commission, still pushes the plan they came up with (which Obama now disavows), and clashes with Grover Norquist. He accepted an advisory position with Goldman Sachs shortly after his retirement from the Senate last year, which would give the OWS crowd a nice heart attack. He could also handily compete with Biden on quotables: In 2010, he called Social Security a “milk cow with 310 million tits.”

Mike Mullen
Republicans have talked about wanting to pull a military superstar like David Petraeus onto a ticket, but this former chairman of the Joint Chiefs of Staff would also be a worthy pick. Bearing in mind that career military men don’t automatically translate to political men — why you don’t see Petraeus on a campaign trail — Mullen was appointed by Bush in 2007 and served through last September, retiring with 43 years in the Navy under his belt. He told NBC News in April that he didn’t want the killing of Osama bin Laden to become overly politicized in the 2012 election. “I do worry a great deal that this time of year that somehow this gets spun into election politics,” he said. “I can assure you that those individuals who risk their lives – the last thing in the world that they want is to be spun into that.” And since it has been spun into that — with tit-for-tats over whether Romney would have made the “gutsy call” — it would be nice to see a military man in the conversation. It also makes one wonder about all the Mullen advice Obama didn’t take.

Jon Kyl
This pick would rank as some seriously handy political timing: The Senate minority whip decides to retire and gets pulled onto the GOP ticket. And yeah, it crossed his mind: “I wouldn’t close my mind to being a vice presidential candidate,” Kyl told reporters upon announcing his retirement. “Having said that, I expect the chances of that are zero.” The Arizona senator has been a fixture of conservative causes in Congress while also stepping out to try to broker agreements in some of the great standoffs of recent congressional times: He got an agreement out of the White House to modernize the nuclear force in return for START treaty approval (an agreement Obama hasn’t kept), but wouldn’t let a bad deal go through the deficit-reduction super committee. And if candidates are picked to bring his or her geographic region along, Kyl could prove valuable in Nevada and New Mexico. Out of this list, Romney would likely see him as the safest pick.

Fred Thompson
Is there life after succumbing to commercials for reverse mortgages? Considering Thompson’s likeability, within the base and beyond, it makes sense to pull the former senator and Law & Order star back onto the campaign trail for another go-round. As he showed with his announcement in 2007, he’s a Tonight Show candidate in a social-media world — which never hurts in the quest to oust an incumbent.