The legislation reprises a plan offered last year that failed to advance.
House Armed Services Committee Chairman Howard "Buck" McKeon, R-Calif., leads the group, which agrees with Defense Secretary Leon Panetta that a looming 8 percent cut to this year's Pentagon budget would recklessly harm the nation's military.
McKeon said the Pentagon faces "dire straits."
The plan would generate replacement savings by requiring a 10 percent reduction in the government's workforce through attrition—replacing one out of every three employees who leave the government.
The automatic cuts, dubbed a sequester in Washington-speak, result from the failure of the 2011 deficit "supercommittee" to meet its assignment to cut the deficit by $1.2 trillion over a decade. This year's $109 billion round of cuts was trimmed by $24 billion in last month's deal to avert the "fiscal cliff," but the Pentagon still faces an 8 percent, $42.7 billion budget cut in the seven months starting in March and ending in September.
The military's top brass warns that the cuts would create a "hollow force" and would devastate military readiness and training. While war costs and salaries for men and women in uniform would be exempt, those exceptions also serve to make the cuts to other Pentagon accounts, like weapons procurement and civilian pay, more harsh.
"Our enemies would love for this to happen," Sen. Lindsey Graham, R-S.C., said.
Non-defense programs face an equal $42.7 billion cut, including a $29 billion, or 5 percent, cut to domestic agencies.
President Barack Obama and fellow Democrats say new tax revenues need to be part of any measure to replace the automatic cuts, which economists warn would slow the economy if allowed to strike on March 1. Obama on Tuesday urged Congress to act to replace the cuts with tax revenue from closing special interest loopholes and with spending cuts elsewhere in the budget.
Senate Democrats are working on a strategy for replacing the sequester, and the subject was a topic at a party retreat in Annapolis, Md., this week. But they have yet to unify behind a plan.
House Republicans, meanwhile, acted twice last year to erase this year's portion of the sequester, most recently in December, when a replacement measure squeaked through the chamber on a 215-209 vote, with 21 Republicans opposed.
But that legislation died with the expiration of the previous Congress. Republicans control eight fewer votes this year, raising questions as to whether they could pass the measure now.
Some tea party conservatives seeking to shrink government are rooting for the cuts to take effect, leading to splits in the party.
"If you feel comfortable cutting the government this way, then you've lost your way as much as the president. What happened to the party of Ronald Reagan who said the No. 1 goal of the federal government ... is to fund the Department of Defense?" Graham said. "What happened to that party? Well I intend to get that party back."