WOLFEBORO, N.H. (AP) - Mitt Romney's wife has disclosed a tantalizing detail about her husband's intensely secret vice presidential search: He's considering choosing a woman.

"We've been looking at that, and I love that option as well," Ann Romney told CBS News in an interview broadcast Thursday. She added: "There's a lot of people that Mitt is considering right now."

She also argued that Obama and his Democrats will "do everything they can to destroy Mitt."

"Early on we heard what their strategy was. It was kill Romney," she said, adding a message to Obama: "Not when I'm next to him you better not."

Romney, for his part, didn't weigh in on that characterization of Obama's strategy during the joint interview. He also declined to describe the status of the vice presidential search, saying: "That's something I'm keeping close with my team."

Speculation is high about who Romney will choose as his No. 2, with his search well under way and his self-imposed deadline for picking a running mate "before the convention" looming large. It's the biggest decision he will make between now and when he accepts the GOP's presidential nomination in late August.

Talk in Republican circles has focused on men as likely top prospects, including Ohio Sen. Rob Portman, former Minnesota Gov. Tim Pawlenty, Wisconsin Rep. Paul Ryan, Florida Sen. Marco Rubio, New Jersey Gov. Chris Christie and Louisiana Gov. Bobby Jindal. But no less than a half-dozen other names also have popped up, including New Hampshire Republican Sen. Kelly Ayotte - who walked in a July Fourth parade with Romney on Wednesday - as well as South Carolina Gov. Nikki Haley, New Mexico Gov. Susana Martinez and former eBay CEO Meg Whitman.

In the interview, Ann Romney also sketched out her own requirements for what she'd like to see in a running mate, saying the person should be "someone that obviously can do the job but will be able to carry through with some of the other responsibilities." She said the person should be someone who will have her husband's back and who he will enjoy being around him and have "the same personality type." She added: "Competent, capable and willing to serve this country. I think there's lots of good people out there that fill that bill right now."

It's been four years since John McCain selected then-Alaska Gov. Sarah Palin, a rock-ribbed conservative who was little-known outside of her home state, to be the first female on a Republican presidential ticket as he sought a way to both fire up the GOP's core supporters while narrowing Democrat Barack Obama's advantage with women voters. It wasn't long before questions about Palin's readiness to be president - and criticism of an inadequate vetting process - became a major problem for McCain, with critics using the pick to pummel the nominee on his decision-making.

This year, Romney has let that experience drive his criteria: He's said preparedness to be president is his No. 1 requirement for a vice president. Unlike four years ago, Republican base voters are energized largely by a desire to beat Obama. But polls show that Romney still badly trails Obama among women and putting one on the ticket - or even just raising the possibility of a female running mate - could help carve into that support.

The Romneys gave the rare joint interview to CBS as they spent the week relaxing with their family at their lakeside estate in Wolfeboro.

Officially, the campaign says that Romney is doing what he's done for the past decade - enjoying family time during a weeklong holiday in New Hampshire. It's also a break from the campaign trail, and a chance to relax before the pre-convention push. But unofficially, the bit of down time is a chance for the contemplative Romney to consider how the campaign is going and adjust strategy as necessary in a contest that polls show is close.

He and his wife huddled Tuesday at the estate for at least 45 minutes with campaign manager Matt Rhoades, senior adviser Beth Myers and top strategist Stuart Stevens on the deck that overlooks the lawn behind his home. Romney's five sons - particularly his eldest son, Tagg - also serve as informal political advisers, and all have been on hand all week, virtually assuring that the campaign and the running mate search were being discussed.

Fueling the running-mate talk was the fact that several potential candidates were essentially auditioning for the spot this week.

Portman was headlining a fundraiser in Concord, N.H., this weekend, and also wrote an opinion piece published in an Ohio newspaper this week to counter Obama's campaign appearances in the state Thursday and Friday. Pawlenty and Jindal both were in Ohio for the same reason, to campaign for Romney near Obama's events.

Romney's vacation ends Sunday when he's scheduled to head to New York for fundraising events - and to resume his campaign schedule fulltime.