The chairman of the Senate homeland security committee on Sunday called on the White House to investigate whether any of its staffers might have been involved in the prostitution scandal that has rocked the Secret Service and Pentagon.

Sen. Joe Lieberman, I-Conn., speaking on "Fox News Sunday," was responding to a push by Senate colleague Charles Grassley, R-Iowa, to find out more about any possible involvement of the White House team. Lieberman went further, urging an internal probe into whether any member of the president's advance team and other personnel could be connected to a scandal that so far has implicated up to 23 people across the Secret Service and military.

"There's no evidence (of White House involvement), but I don't know that the Secret Service is actually investigating that question," Lieberman said Sunday. "I'd say it's a reasonable question and that the White House ought to be conducting its own internal investigation of White House personnel who were in Cartagena, just to make sure that none of them were involved in this kind of inappropriate behavior."

White House spokesman Jay Carney said Friday the administration has no reason to think staffers were involved and implied they would not be looking into the matter.

"From the moment that this was made public and an investigation was launched, we have been in regular touch with the Secret Service and obviously with the Pentagon about this incident," he said. "I'm sure the discussion and the briefing covers a variety of subjects, a variety of both facts and rumors. What I'm not going to do ... is give a play-by-play or speculate about every rumor that you may have heard."

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Carney said he had "no reason to believe" an internal White House investigation would be needed.

But Lieberman said the White House should not be taking Grassley's questions "defensively." He said that members of the White House advance team would know "exactly where the president's going to be at any time," and could be an intelligence target for anybody wishing to attack U.S. figures.

Lieberman said the same about Secret Service agents, warning that the entire incident is "more serious than just a frolic."

"They were not acting like Secret Service agents. They were acting like a bunch of college students away on spring weekend," Lieberman said, noting that any country's enemies could compromise people in security positions "with sex."

Lieberman said his committee is now probing the incident and will hold at least one hearing. While unable to confirm whether cocaine was involved in the night of alleged debauchery, Lieberman said he plans on looking into a rule that Secret Service agents cannot use "intoxicants" within six hours of duty.

Lieberman, also pointing to the spending scandal over pricey conventions at the General Services Administration, said Obama -- while not responsible for the behavior -- is "accountable" for making sure the scandals stop.

"The buck stops at the president's desk. He's the leader of our government. He now has to be acting with a kind of relentless determination to find out exactly what happened and to make sure the people who work for him ... don't let anything happen like this again," Lieberman said.

Obama political adviser David Axelrod, speaking Sunday on CNN's "State of the Union," called the alleged behavior in Colombia "really disappointing."