The Senate on Monday voted to end debate on legislation to repeal cuts to cost of living adjustments for working-age military retirees beginning in fiscal 2016, but it's not clear if the debate is over.

Sen. Roger Wicker, R-Miss., urged all senators to vote on the cloture measure, but challenged Sen. Harry Reid, D-Nev., to deal with amendments to the actual bill being considered.

Wicker has co-sponsored a competing bill that would repeal the COLA cuts but recoup the $6 billion it will cost by closing a tax loophole used by individuals, including illegal aliens, currently costing taxpayers $4 billion annually.

"Vote 'yes' on cloture, but say to the leadership: 'Don't lock [debate on the bill] down this time like you usually do," Wicker told lawmakers. "Allow Republicans and Democrats with other ideas … to bring these ideas to the floor, vote on them, and let the American people see that we can correct this wrong [to military retirees] without adding $6 billion to the deficit."

The bill now up for a vote was introduced by Sen. Mark Pryor, D-Ark., and appears to have broad support among other Senate Democrats.

Unlike the bill co-sponsored by Wicker, which was introduced by Sen. Kelly Ayotte, R-N.H., Pryor's legislation does not provide an offset. Another bill, filed by Sen. Bernie Sanders, I-Vt., would repeal the COLA cut but pay for it with money from the Overseas Contingency Operations Fund, which is exempt from Congress' spending cap.

As it stands now, the law passed as part of the 2014 budget deal worked out between Sen. Patty Murray, D-Wash., and Rep. Paul Ryan, R-Wis., will mean lower COLAs for military retirees under age 62 starting in fiscal 2016. They will get annual COLAs that are 1 percentage point lower than those given to other federal retirees and people on Social Security.

Veterans' advocates say a typical retiree will lose about $80,000 because of the so-called COLA-minus-one provision.

Veterans' groups and military associations have been lobbying hard to strike the provision and have been frustrated by what some see as an attempt to use the issue to gain political points or fit an ideological agenda.

Paul Rieckhoff, head of the Iraq and Afghanistan Veterans of America, said it is clear that both parties and both chambers of Congress are on board with repeal, but less clear if they can rise above party politics to do it.

"Veterans don't want to be used as a political chew toy. Veterans saw enough of that during the government shutdown, and we are tired of it," Rieckhoff said in a statement before the cloture vote.

During debate before the cloture vote, Democrats and Republicans took shots at each other for failing to back the legislation each wanted.

Sen. Jeff Sessions, R-Ala., slammed the Pryor bill for breaking the budget deal commitment to new spending that was not offset by new revenue or cuts elsewhere.

"It's an astonishingly cynical move, really, if you think about it," Sessions said. "We would restore the benefit to veterans without paying for it, without admitting a mistake was made, and not living up to the plain promises made in the Ryan-Murray bill which reinforced … spending limitations."

In December, before the Senate passed the budget deal, Sessions had co-sponsored with Ayotte an original amendment to preserve the full COLAs by closing the tax loopholes.

According to Sessions and Ayotte, the Treasury Department estimates the U.S. is losing more than $4 billion annually to fraud linked to tax credits for non-resident or phantom children. Currently, a taxpayer can list additional children on their tax returns without actually proving they exist. Her measure would require each child to have a Social Security number.

Ayotte said in January that closing the loophole would save about $20 billion over 10 years -- far more than the $6 billion that the COLA cut is projected to save in the same period.

Sen. Mark Begich, D-Alaska, a co-sponsor of Pryor's legislation, accused GOP lawmakers of hypocrisy. He said they will "talk a good game [about] loyalty to the troops, wrap themselves in the flag, and then pivot, qualify things, say the sky is falling, and that we can only pass this bill if we pay for it."

Begich said efforts to repeal the COLA cut failed last month because Republicans insisted it had to be paid for.

"This bill has no 'pay fors'," he said. "Why? Because the men and women of our armed forces have already paid … Too many of them paid the ultimate sacrifices, with their lives."

However the vote on Pryor's bill fares in the Senate, it will next move to the Republican-majority House, where there already are a number of COLA repeal bills awaiting action. One, filed by House Veterans Affairs Committee Chairman Rep. Jeff Miller, R-Fla., counts 41 Democrats among its 114 co-sponsors.