The timing is driven by the pending expiration of three investigative powers unrelated to the Page wiretap issues, including the F.B.I.’s ability to collect business records for an espionage or terrorism case. The draft bill would extend those powers while ending legal authority for a defunct system that gave counterterrorism analysts with the National Security Agency access to logs of Americans’ phone calls.

But the bill, according to people familiar with negotiations over the draft, would make other adjustments that dovetail with the inspector general report — like expanding when FISA judges should appoint outsiders to critique the government’s arguments. Lawmakers could also legally require the F.B.I. to be candid with the FISA court and to correct errors.

By contrast, Senator Lindsey Graham, Republican of South Carolina and the close Trump ally who leads the Senate Judiciary Committee, is focused on further scrutinizing the Russia investigation. Recently, Mr. Graham requested interviews with 17 law-enforcement officials who were subjects of the inspector general investigation.

“Somebody,” Mr. Graham said in an interview, “has to pay a price.”

But similar flaws with surveillance have surfaced before, underscoring that the problems may be systemic rather than unique to the Page applications, current and former officials said.

At the F.B.I., nobody gets credit for investigations that go nowhere, said Robert S. Litt, a former national security prosecutor and general counsel of the Office of the Director of National Intelligence during the Obama administration. That cultural reality creates the risk that investigators will slant FISA applications to more easily secure a judge’s approval.

The bureaucratic problem is not limited to the FISA process, Mr. Litt said, pointing to a scandal years ago over F.B.I. forensics experts overstating their findings in courtroom testimony.

Still, the extra secrecy surrounding surveillance shuts out potential checks. For example, defense lawyers get to scour criminal wiretap applications for problems, creating an incentive for investigators to be scrupulous. But defense lawyers do not get to see FISA applications.