By: FOX News

Lawmakers and veterans groups are stepping up efforts to fight cuts to benefits for military retirees under the bipartisan budget agreement passed by Congress before the holiday break.  

President Obama on Thursday put his signature on the two-year budget bill, which includes a contentious provision to pare down annual cost of living increases in benefits for military retirees under age 62, saving the government an estimated $6.3 billion over a decade.   

Bills were introduced in the House this week by members on both sides of the aisle that would effectively undo pension cuts to military retirees. 

On Monday, Rep. Julia Brownley, D-Calif., introduced a bill that would repeal the provision that curtails annual cost of living increases in benefits that go to military retirees under age 62.

“As a member of the House Veterans' Affairs Committee, I believe our service members, veterans, and their families must receive the benefits they have earned and deserve,” Brownley said in a statement. “These benefits are owed to them without equivocation. That is why I have introduced legislation to repeal the military retiree COLA reduction.”

Rep. Ted Poe, R-Texas, introduced a similar bill on Monday, according to The Hill.It was unclear whether either proposal included provisions to offset the costs of eliminating the cuts. 

Several Republican lawmakers, including Rep. Mike Fitzpatrick, R-Pa., and Rep. Martha Roby, R-Ala., have proposed closing a tax loophole that has allowed illegal immigrants to claim fraudulent cash payments in order to replace the cuts.

The change provoking outrage among military and veteran groups this week would reduce retirement benefits for working-age retirees. Starting Dec. 1, 2015, cost-of-living adjustments for pensions of people under 62 would be modified to equal inflation minus 1 percent; then at 62, retirees would receive a "catch-up" increase that would restore their pensions to reflect levels as if the cost-of-living adjustment had been the full consumer price index in all previous years. 

But they wouldn't get back what was lost, meaning a reduction of nearly $72,000 in benefits over a lifetime for a sergeant first class who retires at age 42, by one group's estimate. Sen. John McCain, R-Ariz., said a veteran of identical rank who retired at 38 would still wind up with $1.62 million in retirement pay over a lifetime.

But officials have said repeatedly in recent years that changes in the system would not affect current military members or retirees. Rather, they would be applied to future recruits.

"Keep your promise" was the theme of a lobbying effort by the Military Officers Association of America.

American Legion National Commander Daniel M. Dellinger said the group was "horrified" that the Senate could pass a bill "so unfair to those Americans who have served honorably in uniform."

The Veterans of Foreign Wars predicted the change would prompt an exodus of those at midcareer once the U.S. economy rebounds, and that it will hurt efforts to recruit new people into the all-volunteer force.