But the committee's chairman, Representative Bart Gordon, Democrat of Tennessee, said the proposal represented "a radical change" and "has raised as many questions as it has answered".
The subcommittee chairman, Representative Brian Baird, a Washington Democrat, disagrees.
The hearing chairman, Representative Darrell Issa, rightly criticized the A.T.F.'s failure.
Its chairman, Representative Jim Jordan of Ohio, has said he will not support Mr. Boehner's bill.
The committee's chairman, Representative Howard McKeon, is an avowed foe of Pentagon cost-cutting.
Mr. Stupak and the committee chairman, Representative Henry A. Waxman, Democrat of California, signed the letters.
"We're trying to find some common ground," said the chairman, Representative Doc Hastings, Republican of Washington.
The committee chairman, Representative Ike Skelton, Democrat of Missouri, looked irritated and bewildered.
"The response has been dynamic," said the committee's chairman, Representative Robert W. Ney, Republican of Ohio.
The panel chairman, Representative Bart Stupak, Democrat of Michigan, said, "No one is in charge here".
The committee's chairman, Representative Darrell Issa, has treated this refusal as a cover-up of wrongdoing by the Justice Department.
