But the former Massachusetts governor suggested a lack of leadership led to the scandal and left no doubt what he'd do if it had happened on his watch.
"I'd clean house," Romney told radio host Laura Ingraham. "The right thing to do is to remove people who have violated the public trust and have put their play time and their personal interests ahead of the interests of the nation."
Among key Republicans on Capitol Hill, there was support for Sullivan and deference to his investigation — a recognition by some in Congress that the scandal needs no spinning and that any congressional action must have credibility with voters.
It's about national security, Republicans say. But there's no question the hubbub also is about illicit sex, a topic not eagerly discussed by a long list of lawmakers who have transgressed in that department.
Louisiana Republican Sen. David Vitter, for example, admitted in 2007 to a "serious sin" after his telephone number had appeared in the records of a Washington-area escort service that authorities said was a front for prostitution. Vitter, a member of the Armed Services Committee, won re-election in 2010.
Asked how much responsibility Obama should be taking for the scandal, House Speaker John Boehner demurred, saying he's interested right now in finding out just what happened in Cartagena. A pair of aggressive House chairmen have deferred to the Secret Service probe, promised to monitor it and left open the prospect of launching their own highly public investigations.
Across the Capitol, Iowa Republican Sen. Chuck Grassley, one of his chamber's most dogged investigators, made public a letter to Sullivan that implied he believed more U.S. personnel in Cartagena that week were worth investigating. As examples, Grassley named the White House Communications Agency and the president's advance staff. Was Sullivan investigating them?
"If not, why not?" Grassley wrote.
A 12th member of the military, assigned to the WHCA, was implicated in the scandal and on Monday was relieved of his duties at the White House. Presidential spokesman Jay Carney, meanwhile, confirmed that the White House counsel had done his own investigation and ruled out any misconduct among White House employees who helped arrange Obama's trip.
Distancing the White House from the scandal, Carney said the internal investigation was conducted out of an abundance of caution and not as the result of evidence of misconduct. And he made clear, over and over again, that WHCA, despite its name, is a military unit and not a White House one.
The gender politics that have infused every phase of the 2012 election make the issue especially sensitive.
"I can't help but wonder if there'd been more women as part of that detail if this ever would have happened," Sen. Susan Collins, R-Maine, said Sunday on ABC News' "This Week."
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