"It's important for us, if we're going to proceed legislatively, to keep in mind there's a price to be paid for that, and it might well in fact do irreparable damage to our capacity to collect information," Mr. Cheney said.

The administration, backed by Republican leaders in both houses, has also resisted calls for inquiries by either Congress or an independent investigator.

As for the politics, some Republicans say they are concerned that prolonged public scrutiny of the surveillance program could prove a distraction in this year's midterm Congressional elections, and the administration has worked to contain any damage by aggressively defending the legality of the operation. It has also limited its Congressional briefings on the program's operational details to the so-called Gang of Eight -- each party's leaders in the Senate and the House and on the two intelligence committees -- and has agreed to full committee briefings only on the legal justifications for the operation, without discussing in detail how the N.S.A. conducts it.

Ms. Wilson said in the interview Tuesday that she considered the limited Congressional briefings to be "increasingly untenable" because they left most lawmakers knowing little about the program. She said the House Intelligence Committee needed to conduct a "painstaking" review, including not only classified briefings but also access to internal documents and staff interviews with N.S.A. aides and intelligence officials.

Ms. Wilson, a former Air Force officer who is the only female veteran currently in Congress, has butted up against the administration previously over controversial policy issues, including Medicare and troop strength in Iraq. She said she realized that publicizing her concerns over the surveillance program could harm her relations with the administration. "The president has his duty to do, but I have mine too, and I feel strongly about that," she said.

Asked whether the White House was concerned about support for the program among Republicans, Dana Perino, a presidential spokeswoman, said: "The terrorist surveillance program is critical to the safety and protection of all Americans, and we will continue to work with Congress. The attorney general testified at length yesterday, and he will return to Capitol Hill twice more before the week ends."

Aides to Representative Peter Hoekstra of Michigan, who as chairman of the full House Intelligence Committee is one of the eight lawmakers briefed on the operations of the program, said he could not be reached for comment on whether he would be open to a full inquiry.