WASHINGTON — The fractious debate over restarting the government’s sweeping surveillance program is expected to reach its final Senate showdown on Tuesday, when defense hawks make an urgent appeal to preserve more power for security agencies to gain access to Americans’ phone records.

But if the hawks prevail and push too far, many members of the House said they would reject the Senate approach, meaning that the surveillance program would remain largely blacked out until a compromise was reached. The program lapsed at 12:01 a.m. Monday because opponents of surveillance refused to extend it through the legislative fight.

Senator Mitch McConnell of Kentucky, the majority leader, and an ally, Senator Richard Burr of North Carolina, the Intelligence Committee chairman, plan one last attempt to amend the USA Freedom Act, which the House passed and which the two senators once denounced as an impediment to national security. Both men have declared the bill a dangerous retrenchment from national security programs put in place after the attacks of Sept. 11, 2001, even though the House overwhelmingly passed the legislation, with the backing of both Speaker John A. Boehner, Republican of Ohio, and President Obama.

The White House on Monday pressed for the Senate to refrain from making substantive changes to the legislation, arguing that with the authorizations lapsed, this was no time to add provisions that could lead to a lengthy parliamentary back-and-forth on Capitol Hill.