House Majority Leader Kevin McCarthy outlined next week's schedule.
An amendment to allow flag displays is "appalling," he said.
The bank will expire at the end of June absent congressional action.
House Democrats have been licking their wounds following a disastrous 2014 election cycle.
Steny Hoyer said the freeze made sense in the past, but may limit those who run for office.
"Obviously, there are some things we can do," the Democratic whip said.
House Democratic leaders are lining up against fast-track.
Hoyer, Pelosi both offered their backing of the Corker-Cardin deal.
Dems see Boehner as a willing compromiser.
Vocal Kremlin critic Boris Nemtsov was shot in Moscow last week.
A House microphone picked up Hoyer calling McCarthy a "coward" Thursday night.
Hoyer applauds strategy, though his support is qualified.
“I think this is just wishful thinking of the members," House Majority Leader McCarthy said.
Opponents include House Majority Leader Kevin McCarthy, the No. 2 Republican in the House.
The Democrat said proposed amendments in the Senate could kill the bill.
The freeze on salaries for members of Congress has been in place since 2010.
D.C.-area lawmakers say funding should be left intact while safety issues are resolved.
House Majority Leader McCarthy and House Minority Whip Hoyer discussed the upcoming week's agenda.
The House will consider cybersecurity legislation next week.
Enthusiasm builds among reformers even as White House clarifies president's remark.
The minority leader is worried about Dems leaving the House to run for the Senate.
House Democrats said they expect the Speaker to bring a "clean" DHS bill to the floor.
The No. 2 House Democrat appeared to let his feelings slip too close to the microphone.
House Minority Whip Steny Hoyer (D-Md.) suggested that Republicans are behaving like children.