WASHINGTON — Mitt Romney’s vice presidential search has entered a new phase: auditions.

As his campaign evaluates potential running mates, Republicans with a possible shot at the No. 2 spot on the presidential ticket are starting to engage in unofficial public tryouts for the traditional vice presidential role of attack dog.

Democratic President Barack Obama is “the most ill-prepared person to assume the presidency in my lifetime,” New Jersey Gov. Chris Christie declared in a speech in Kentucky this week. Florida Sen. Marco Rubio told South Carolina Republicans that there hasn’t been such a “divisive figure in modern American history” as Obama.

Wisconsin Rep. Paul Ryan, speaking Tuesday at the Ronald Reagan Presidential Library — it’s a favorite venue for Republicans seeking more attention — said Obama “wants to take us further in the wrong direction.” In an Alabama appearance this month, Louisiana Gov. Bobby Jindal called Obama “the most incompetent president since Jimmy Carter.”

Not that any of them — or any of the others who may have landed a spot on Romney’s list — are talking about becoming vice president. Nor are any of them acknowledging that they’re trying out for the role or saying the Romney campaign has asked them to do so. Top Romney aides are sworn to secrecy, as are potential running mates and their staffs — an example of the Romney campaign’s closely controlled, no-leaks culture.

But their high-profile appearances come more than a month after Romney assumed, for all practical purposes, leadership of the Republican Party. His vice presidential search is well under way, with his Boston headquarters engaged in a secretive process of weighing the pros and cons of each potential pick.

With three months to go until Republican National Convention, his campaign has little time to waste as it meticulously prepares the presumptive Republican nominee to make one of his most important decisions. With it will come implications not just for whether he’ll win the White House but how he would govern.

Knowledge of the process is limited to a few of Romney’s highest-level aides. Information is on a “need-to-know” basis — and as far as those aides are concerned, there are few people inside the Boston headquarters at 585 Commercial St. who need to know, let alone reporters and other outsiders. The Republicans who discussed the vice presidential selection process did so on the condition of anonymity because the campaign has barred staff from talking about the selection in public.

The process is so secret because it’s so sensitive. A vice presidential vetting is possibly the most intense background check in politics. Everything is fair game: voting records and the political past, to be sure, but also personal issues.

“You’re sitting down with someone and asked if they’ve ever had a marital problem, if their spouse has ever cheated on them, if they’ve ever sought mental health counseling — that’s just the beginning,” said Sara Fagen, who worked for President George W. Bush and for Romney’s 2008 presidential campaign.

If past campaigns are an indication, that level of probing will happen later, after Romney’s campaign has narrowed the list to a few people who are under serious consideration. Earlier in the process, potential choices are typically asked fewer invasive biographical questions, as the campaign itself runs through all available public information.

This more basic information will help the campaign narrow the list — and evaluate and prepare to deal with potential trouble spots in the backgrounds of those who make it through. The campaign team will have to be prepared to deal with past statements that might publicly contradict Romney or give Obama’s team an extra opening to criticize his Republican opponent. The Democratic president had to deal with this in 2008, when Republicans gleefully circulated a clip of Joe Biden, now Obama’s vice president, saying Obama was “not ready” to be president.

The Republicans who are informally auditioning each would bring different strengths — and drawbacks — to the ticket.

Ohio Sen. Rob Portman supported Romney early, has a solid rapport with the candidate and hails from a critical battleground state that could decide the election. But he wouldn’t necessarily appeal directly to Hispanic or women voters.

Jindal, the Louisiana governor, could help Romney turn out the religious right and would add diversity to the ticket as an Indian-American, but he struggled during a national debut rebutting the 2010 State of the Union address.

Virginia Gov. Bob McDonnell appeals to social conservatives but signed a controversial state law that requires Virginia women to have an ultrasound test before an abortion.

New Hampshire Sen. Kelly Ayotte, who’s campaigned frequently with Romney, could help with female voters and in her swing state of New Hampshire. But she’s from New England, the same region of the country as Romney, while Christie, a conservative favorite who can work a crowd, is from New Jersey.

Rubio could bring Florida, always a deciding factor in a general election, and appeal to Hispanics, a fast-growing voting bloc, but he’s run into some trouble over a foreclosed home and possible misuse of an official credit card. Ryan is a serious, leading policy mind with a bright future. But while Romney has endorsed the Wisconsin congressman’s controversial budget, picking Ryan could shine a brighter spotlight on a plan that would make major changes to Medicare.

As deliberations and the informal auditions continue, potential candidates are perfecting their non-denial denials about providing any information to the Romney campaign.

“The Romney campaign has a policy, and I’m a national co-chair of the campaign, that we don’t talk about the vice presidential policy in terms of timing whether it relates to me or anyone else or the aspects of that,” former Minnesota Gov. Tim Pawlenty, another possible pick who was featured in a new ad Romney released Thursday, told MSNBC last week when asked if he’d agreed to be vetted. “That’s just the campaign policy. We don’t discuss the details of that process.”

“I’m not getting into that. I’m not changing any of my answers,” Ryan told the Washington Examiner’s editorial board recently when asked about the process. “I get asked this every time I walk down the street. I’m not giving you any answers.”

Or they’re not saying anything at all. After a speech at the U.S. Chamber of Commerce on Wednesday, reporters questioned Rubio about whether he was being considered for vice president.

“Senator, would you like to answer any questions about vice president?” one reporter asked.

Rubio, smiling, turned and walked away.