Sen. Sessions tries to undo cuts to military retiree benefits ahead of Senate budget vote Oct. 17, 2013: (L to R) Sen.Jeff Sessions, R-Ala., Rep.Paul Ryan, R-Wis. and Sen. Patty Murray, D-Wash. emerge from an informal meeting of Congressional budget conferees at the U.S. Capitol.Reuters A top Republican senator is trying to undo cuts to military retiree benefits in the House-passed budget deal ahead of a crucial vote Tuesday morning in the Senate. Alabama GOP Sen. Jeff Sessions filed an amendment late Monday to restore money that was cut from veteran and military retiree pension benefits by closing a loophole that allowed illegal immigrants to qualify for child tax credits. His move comes after several GOP senators voiced complaints about the budget package, which sailed out of the House last week on a strong bipartisan vote. Now it appears America's veterans and military retirees could be a determining factor in whether the deal makes it through the Senate. Republicans say the plan unfairly forces veterans to pick up the cost of new spending. "It's unacceptable to single out our men and women in uniform in this way," said Sen. Kelly Ayotte, R-N.H. In sharp contrast to the confident statements issued by House leaders ahead of their vote last week, Senate leaders indicated they were still corralling support. Democrats need to hold most of their caucus of 55 senators together and pick up a handful of GOP senators in order to reach the 60-vote threshold to advance the bill on Tuesday. The Republican "no" votes were piling up over the weekend. Ayotte, Sessions and other senators focused largely on the cuts to veterans and military retirees. Sessions" amendment would restore the funding by requiring applicants for a particular child tax credit to submit their Social Security numbers. Federal law bars illegal immigrants from collecting tax benefits but that particular tax credit is often claimed by undocumented residents, according to recent watchdog reports. Sessions' office has estimated that closing the tax credit loophole would save the government approximately $4.2 billion, the amount the Treasury Inspector General for Tax Administration reported that illegal immigrants received due to the credit in 2010.