The package could also hamstring the Office of Congressional Ethics, which undertakes bipartisan inquires about lawmakers’ conduct and makes recommendations for discipline to the Ethics Committee. One proposed change would impose term limits for board members, which would result in the removal of all but one Democrat as the panel considers whether to begin an inquiry into certain Republican congressmen over their conduct related to the Jan. 6, 2021, attack on the Capitol.
Another proposal would mandate that the office hire investigators within the first 30 days of a new Congress, a requirement some ethics experts fear could leave the office understaffed for lengthy periods if hires are not made within that time frame.
Mr. McCarthy has also called for a “Church-style investigation” into past abuses of power by the Federal Bureau of Investigation and the Central Intelligence Agency. It is a reference to the select committee established in 1975, informally known by the name of the senator who led it, Frank Church of Idaho, that looked into abuses by American intelligence agencies.
He toughened his language in response to hard-right demands to oust Alejandro N. Mayorkas, the homeland security secretary, calling on him to resign or face potential impeachment proceedings. He promised Representative Marjorie Taylor Greene of Georgia, who was stripped of her committee assignments for making a series of violent and conspiratorial social media posts before she was elected, a spot on the coveted Oversight Committee.
Mr. McCarthy threatened to investigate the House select committee looking into the Jan. 6 attack, promising to hold public hearings scrutinizing the security breakdowns that occurred. Last month, he publicly encouraged his members to vote against the lame-duck spending bill to fund the government.
It is unclear whether any single offering from Mr. McCarthy at this point would be enough to win over some lawmakers.
During the call on Sunday, Representative-elect Mike Lawler of New York, who has announced his support for Mr. McCarthy, pointedly asked Representative Matt Gaetz of Florida, a ringleader of the opposition, whether he would vote for Mr. McCarthy if the leader agreed to lower the threshold for a vote to oust the speaker to just one member of Congress. Mr. Gaetz was noncommittal, according to a person on the call who recounted it on the condition of anonymity.