A final effort by Senate Republicans to halt cuts to pensions of military retirees failed late Tuesday, after Democrats blocked an amendment to the controversial budget bill.

The two-year budget agreement, which cleared a key test vote earlier in the day, was expected to get a final vote no later than Wednesday.

Ahead of the final vote, Sen. Jeff Sessions, R-Ala., tried unsuccessfully to use a parliamentary tactic to force a vote on the amendment, which he wrote to undo the cuts for military retirees.

A provision in the already House-passed bill would cut retirement benefits for military retirees by $6 billion over 10 years.

Sessions wanted to instead eliminate an estimated $4.2 billion in annual spending by reining in an IRS credit that illegal immigrants have claimed.

He and fellow senators argued the bill unfairly sticks veterans and other military retirees with the cost of new spending.

“It’s not correct, and it should not happen,” Sessions said on the floor.

"By blocking my amendment, they voted to cut pensions for wounded warriors," he said afterwards. "Senators in this chamber have many valid ideas for replacing these pension cuts, including my proposal to close the tax welfare loophole for illegal filers, and all deserved a fair and open hearing. But they were denied.”

Sessions’ office claimed the vote Tuesday to block the amendment was a vote to "cut military pensions instead of cutting welfare for illegal immigrants."

Senate Budget Committee Chairman Patty Murray, D-Wash.,who brokered the budget deal with House counterpart Rep. Paul Ryan, R-Wis., argued the GOP effort was really an attempt to kill the entire bill.

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The Republican-led House passed the bill last week in an effort to avoid another stalemate leading to a potential government shutdown, like the one in October that polls showed was largely unpopular with voters.

The two-year budget deal would ease for two years some of the harshest cuts to agency budgets required under automatic spending curbs commonly known as sequestration. It would replace $45 billion in scheduled cuts for the 2014 budget year already underway, easing about half of the scheduled cuts.

The Associated Press contributed to this report.