(CNSNews.com) - Despite having overseen the National Security Agency's controversial domestic surveillance program, Michael Hayden is "increasingly likely" to be confirmed as the new director of the Central Intelligence Agency, according to the top Democrat on the U.S. House Intelligence Committee.

U.S. Rep. Jane Harman from California is one of many Democrats in the House expressing reservations about Hayden, even as he appears headed for Senate confirmation.

"There are some issues with Mike taking over the CIA," Harman told a Brookings Institution audience Monday. "The failure to clarify the legal underpinnings of the (domestic surveillance) program, to make certain that the underpinnings are sound, will always make one suspicious, including me," she added. "Either they are hiding something now, or they will be hiding something tomorrow."

On May 11, USA Today reported that the National Security Agency (NSA) had built a database of telephone call records with the help of three major U.S. telecommunications companies. Since the report was published, BellSouth and Verizon have denied its accuracy and BellSouth has demanded a retraction.

Still, on Monday Harman blamed the Bush administration for failing to get warrants from the Foreign Intelligence Surveillance Act (FISA) Court, before conducting the surveillance of suspected al Qaeda operatives.

"This program must fully comply with the exclusive law that Congress passed -- the Foreign Surveillance Intelligence Act -- that requires court warrants, that requires congressional oversight," Harman said. "That is to make sure that the civil liberties of Americans are being protected, while giving us the capabilities to find the bad guys even if they are next door."

George J. Terwilliger III, former deputy attorney general under President George H.W. Bush, joined Harman at the Brookings Institute event in Washington D.C., and complained that the debate over the domestic spying program has been the subject of "incredibly overheated political rhetoric."

Surveillance "is the fundamental building block of putting together information about a cell or a network of any stripe, including a terrorist cell," Terwilliger said, adding that the information contained in the NSA database is similar to the information on a person's monthly phone bill. That information, Terwilliger said, does not require a warrant.

The FBI and intelligence community have "been able to access that information for years," he said.

Terwilliger also argued that Congress should not necessarily be briefed on every aspect of the surveillance program. "The nature of spying is clandestine, it is secret. Congress is not very good at keeping secrets," he said.

During his confirmation hearings last week, Hayden said the NSA was following the president's orders in conducting the surveillance program. "We're going to do exactly what he said, and not one photon or one electron more," Hayden reportedly told members of the Senate Intelligence Committee.

"And I think that's what we've done," he added.

In January, Hayden explained to a National Press Club audience that the "NSA intercepts communications, and it does so for only one purpose -- to protect the lives, the liberties and the well-being of the citizens of the United States from those who would do us harm."

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