Democrats, about to take control of Congress, say they will forge a bipartisan compromise to put limits on President Bush’s program of domestic eavesdropping of suspected terrorists.

Democrats say they already have a starting point for a compromise, noting that bipartisan proposals this year require court warrants for eavesdropping. At the same time, party leaders will be treading carefully in an effort to assure Americans that they can protect privacy without sacrificing vigilance, and to discredit Republican charges they are weak on national security.

“How will the Democrats proceed? I think gingerly,” Steven Aftergood, who directs a government secrecy project for the Federation of American Scientists in Washington, said. “They can no longer function as a protest group.”

After the September 11, 2001, attacks, Mr. Bush authorized the National Security Agency to eavesdrop without getting court warrants on communications between suspected Al Qaeda operatives in America and overseas.

While disclosure of the program triggered criticism from both parties, practically no chance exists that the Republican-controlled Congress that returns to Washington next week will act on the issue, leaving it for the next Congress that convenes in January.

Senator Rockefeller, a Democrat of West Virginia who will head the Senate Intelligence Committee, said in an interview that Congress may be able to pass bipartisan legislation in six months.

Mr. Rockefeller said he supports “collection of conversations where that is necessary for national security” but is disturbed by “blanket” eavesdropping.

The next Senate Judiciary Committee chairman, Senator Leahy, a Democrat of Vermont, said the administration needs to provide more information to lawmakers about the program; Congress has been asked to “legalize secret, unlawful actions that the administration has refused to fully divulge.”

To pass legislation next year, Democrats will have to bridge a gap between lawmakers who favor requiring a search warrant in each case of surveillance and those who would permit broad court authorization.

Democrats such as Senator Feinstein of California have made individual warrants a prerequisite. Republicans say that would hobble the NSA’s ability to move quickly.

Mr. Bush agreed in negotiations with the judiciary committee chairman, Senator Specter, a Republican, to authorize a special court that oversees intelligence and operates in secret to decide whether the eavesdropping was legal. The court was created under the 1978 Foreign Intelligence Surveillance Act to review, behind closed doors, requests for eavesdropping on suspected spies, terrorists and other foreign agents.

Mr. Specter’s measure stalled this year, as did a House-passed bill to permit surveillance on condition that the president brief leaders of Congress.

Most Democrats opposed both measures, arguing that they failed to protect privacy and insisting that the 1978 law remain the exclusive means for authorizing surveillance. At the same time, no one in Congress has called for Mr. Bush to halt the program.

Democrats risk a political backlash “if they tie the president’s hands and if there are more attacks,” Robert Turner, who directs the center for national security law at the University of Virginia law school in Charlottesville, said. Any legislation must not “require unplugging the headphones for a period of hours, days or weeks while some judge finds time to look at the paperwork,” Mr. Turner, who supports the president’s program, said.

A member of the Intelligence and Judiciary committees, Ms. Feinstein would require the NSA to submit requests to the special court created under the 1978 law. Her legislation would permit emergency eavesdropping for seven days while a warrant is sought. Mr. Specter supports her proposal as an alternative to his own.

A separate House measure proposed by Rep. Adam Schiff, a Democrat of California, and Jeff Flake, a Republican of Arizona, would also require specific warrants and force Mr. Bush to tell congressional committees who is being wiretapped and why.

The measure “has broad bipartisan support and would probably be a starting point” for debate next year, a spokeswoman for House speaker-designate Nancy Pelosi of California, Jennifer Crider, said.

Mr. Bush’s allies say it is impractical to force the NSA to seek warrants because it must act quickly to sift through a large volume of messages. “Something like that simply would not work,” the intelligence committee chairman, Senator Roberts, a Republican of Kansas, said in an interview.

The director of the American Civil Liberties Union’s Washington office, Caroline Fredrickson, urged congressional hearings to “grapple with this immediately.”

A U.S. appeals court is reviewing a ruling by a federal judge in Detroit declaring that the NSA program is illegal. Justice Department Inspector General Glenn Fine told Congress this week that he will investigate the agency’s “compliance with legal requirements governing the program.”

Civil libertarians say that, with the midterm congressional elections over, they may pick up support from such Republicans as Senators Craig of Idaho, Murkowski, of Alaska, and Sununu of New Hampshire, who have voiced concern about the surveillance.

“The limited-government types and the strong-executive types” are split, increasing chances some Republicans will support constraints on the spying program, a University of Chicago law school professor who favors court supervision of the surveillance, Richard Epstein, said.

The longer Congress waits, he said, “the longer becomes the implied ratification that the president is within his rights.”