Republicans say Rep. Cathy McMorris Rodgers (Wash.) has a bright future in the House. An able messenger who brings diversity to the party’s public face, she has a good shot at becoming Conference chairwoman in the next Congress.

“She’s able to give a view that others have not been able to,” House Rules Chairman David Dreier (R-Calif.) said.

But behind the scenes, her supporters are pushing for something bigger: the vice presidency. And for them, last week’s controversy over a Democratic operative’s swipe at Ann Romney, the wife of GOP presumptive nominee Mitt Romney, allowed McMorris Rodgers to step into the spotlight as a Romney surrogate, providing her national exposure.

Quickly after Hilary Rosen, a managing director at SKDKnickerbocker, said on CNN last Wednesday that Ann Romney had “never worked a day in her life,” McMorris Rodgers slammed the comment, tweeting “Wrong. Being a mom is a full-time job.”

Just hours before Rosen’s comments ignited the Internet and social media worlds, the Romney campaign had sent out a release with the subject line “Cathy McMorris Rodgers: President Obama’s Policies Are Not Working For Women.”

Independent public polling has shown a wide gap between Romney and President Barack Obama among female voters. The timing of Rosen’s comments and the Romney campaign’s deployment of McMorris Rodgers, the lone woman among the GOP’s top House leaders, as a surrogate shows the currency of the issue.

Regarding the vice presidency, McMorris Rodgers, Romney’s campaign chairwoman in Washington state, said: “I’m really not expecting to get that phone call. I’m not seeking that phone call” and that it’s “just not on my radar screen.”

However, after National Journal’s Hotline left McMorris Rodgers off of its “Veepstakes Power Ratings,” the Hotline staff placed her as a “plausible alternative,” ranking her at No. 10. The Hotline staff explained that they “got a call from a McMorris Rodgers ally urging us to reconsider” after they first left her off of the list. Late last month, a mysterious email from dcpress2012@gmail.com to Washington, D.C., media, including Roll Call, boosted her as a vice presidential candidate.

“I think she is a smart and capable politician. It may make political sense to pick her,” said Terry Nelson, who served as the political director of the 2004 Bush/Cheney campaign. Nelson cautioned that “we are so far off from a decision, and certainly the politics may change between now and then. There are also many issues that the Romney team will have to balance, and gender may end [up] looking less important than it does now.”

For now, at least, the gender issue is at the forefront. And even before last week’s flare-up, McMorris Rodgers was spending time refuting the Democratic talking point that the Republican Party is waging a “war on women.”

At a March 22 breakfast hosted by Romney, McMorris Rodgers told the former Massachusetts governor, “Don’t let this issue scare you.” The statement was greeted with applause.

“Republicans won the women’s vote in 2010! It’s not a headline that a lot of papers ran,” McMorris Rodgers said in an interview at her office in the Rayburn House Office Building. She also argues that reports of political damage to the GOP from recent episodes on women’s issues, such as this year’s fight over the Obama administration’s contraception rules, are overblown.

A common sentiment communicated to Roll Call in background and off-the-record conversations is that McMorris Rodgers offers appeal to female voters, and, because of her background, to blue-collar voters.

McMorris Rodgers grew up on a 12-acre orchard, selling fruit from the family truck. She worked her way through Pensacola Christian College, a strict Baptist school with a “no-touch” policy between members of the opposite sex. “I got in trouble at PCC a couple of times,” she said.

At 24, she was appointed to represent a rural district in the Washington state House. One key constituent concern was cougars stalking farm animals. But she also led a bitter fight to prevent state employees from unionizing. In 2002, she was elected Minority Leader, the first woman to lead either party in the state House.

That year she told the Spokane Spokesman-Review that she had no aspirations for higher office, but a subsequent phone call from then-Rep. George Nethercutt (R), who was leaving Washington’s 5th district to run for Senate, changed her mind. In 2004, she won Nethercutt’s seat.

Now in her fourth term, she has some experience on Capitol Hill to balance Romney’s image, but not too much. She’s a “surprise” but not a “shock,” given her familiarity with the D.C. press corps, proponents argue.

McMorris Rodgers is one of at least three top female candidates Romney’s team could consider, with the others being New Mexico Gov. Susana Martinez and New Hampshire Sen. Kelly Ayotte.

Neither Martinez nor Ayotte have spent much time in front of the public eye, which a GOP leadership aide said could lead to problems: “Exhibit A: Sarah Palin.”

The aide described McMorris Rodgers as “Republican woman version 3.0.” Palin was charismatic and conservative but wilted under the spotlight. Minnesota Rep. Michele Bachmann was charismatic and conservative but highly polarizing. McMorris Rodgers strikes a balance of conservatism, experience and effective messaging, the thinking goes.

However, some of the (mostly male) GOP operatives consulted on the question offered harsh verdicts of her chances.

“It’s a little silly for them to play that card,” one said.

“I think she has a very bright future, but I’m not sure she would be in the top 10 this cycle,” a second said.

“1-in-1,000 chance,” a third said.

These sources pointed out that House Members are rarely picked, that Washington state is all but certain to go to Obama, that McMorris Rodgers hasn’t faced — and might not be ready for — the unrelenting scrutiny of the presidential race and that she isn’t well-known nationally.

John Dunagan, a Republican strategist and senior vice president at DDC Advocacy, said: “I don’t think it’s impossible. I think it’s probably unlikely.” Dunagan also noted a potential pitfall: Picking a woman could “feed the narrative” that Romney is struggling with female voters, he said.

Either by accident or design, the discussion could raise McMorris Rodgers’ profile and help her ascent in the House. Republicans said leadership is happy to have a woman as part of the party’s public face, and some spoke of plans to raise her profile. “You’ll hear a lot more from her in the next couple of months,” one GOP Member said.

“I’m interested in running for Conference chair,” McMorris Rodgers said. “And I’m going to be looking at that and talking to Members. [Current Conference Chairman] Jeb Hensarling [Texas] is going to be looking at Financial Services [Committee], so I think there will be an opening there,” she added.

Speaker John Boehner (R-Ohio) backed her for Conference vice chairwoman in 2008, and she was re-elected unanimously in 2010. Her focus has mostly been on messaging, not on steering the party’s direction, GOP sources said.

McMorris Rodgers is known for coining catchy talking points, and she has succeeded in bringing Republicans up to speed on new media, personally meeting with every Member to encourage them to use Facebook and Twitter. She recently opened an event with conservative bloggers by welcoming the moderator, the Heritage Foundation’s Robert Bluey, as her 10,000th follower. She also turned her Capitol hideaway office into a social media headquarters called “GOP Labs,” where aides work on videos and monitor the Web.