A Senate committee debated Thursday whether to pass legislation to create a Department of National Homeland Security and establish a White House office to combat terrorism.

Such a department would elevate the position of homeland security director to Cabinet-level status.

The debate over the status of homeland security chief Tom Ridge emerged last month when Senate leaders complained about Ridge refusing to give formal testimony to the Senate Appropriations Committee, which will determine whether to fund the president's $38 billion request for homeland security.

Sen. Robert Byrd, D-W.Va., wants Ridge to testify, but Ridge and the White House have said that he is not required to give formal testimony because he is a presidential adviser, and that would violate the separation of powers clause of the Constitution.

On Capitol Hill Wednesday to meet with lawmakers in the House Appropriations Committee, Ridge said the battle is one that predates the Bush administration.

"I understand this debate about advisers to the president, and the separation of powers is a debate in a democracy that been going on, not just in this administration. It's been going on for 50 to 60 years," he said.

At the Senate Government Affairs Committee hearing Thursday, Republicans agreed that something needs to change. Sen. Fred Thompson of Tennessee said that with the size and scope of Ridge's duties and potential budget, "We can't stay where we are" in terms of Ridge's inaccessibility to open hearing questions.

At Thursday's hearing, the president's budget director, Mitch Daniels, said the administration is "very open" to alternative arrangements for Ridge's office.

But on the other side of the Capitol, Ridge continued his business as usual, delivering the second of two informal, closed-door House committee briefings — this one to the House Government Reform Committee.

This briefings have satisfied House Republican leaders, but Democrats are unmollified by the director's closed-door appearances.

Rep. Henry Waxman, D-Calif., said he hasn't really learned anything from Ridge's latest briefing.

House Minority Leader Dick Gephardt told President Bush in a letter Thursday that many lawmakers are learning about the administration's anti-terror activities through the media, and called for more frequent consultations between the executive and legislative branches.

After the meeting, Ridge summarized for reporters what issues arose in his briefings on the Hill.

"Much of yesterday was about how the office operates, how it is funded, who's working where. Today's discussion touched that a little bit but we really talked about port security and aviation security; about information fusion and intelligence gathering; continuity of government operations and a fairly exhaustive list of subjects."

Ridge's meeting was the 36th or 37th closed-door meeting with lawmakers, Ridge said, adding that he is happy to give more informal briefings.

Fox News' Brian Wilson and James Rosen and the Associated Press contributed to this report.