"That's clearly putting the cart before the horse and clearly having things backwards in a dysfunctional process," Vitter said.

Vitter ran into opposition from Democrats and some Republicans. 

Sen. Mark KirkMark Steven KirkHigh stakes as Trump heads to Hill Five things to watch for at Trump-Senate GOP meeting Giffords, Scalise highlight party differences on guns MORE (R-Ill.) said Tuesday that Vitter’s objection ought to be waved since the VA funding bill adheres to a budget proposal put forth by House Budget Committee Chairman Paul RyanPaul Davis RyanRepublicans are avoiding gun talks as election looms The Hill's 12:30 Report Flake to try to force vote on DACA stopgap plan MORE (R-Wis.). That plan passed the Republican controlled House but failed in the Senate earlier this year.

"I would put forward that this bill is rather unique because it conforms to the budget," said Kirk. "It conforms to the Paul Ryan budget that passed the House on April 15."

Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsUnder pressure, Trump shifts blame for Russia intrusion Overnight Tech: Judge blocks AT&T request for DOJ communications | Facebook VP apologizes for tweets about Mueller probe | Tech wants Treasury to fight EU tax proposal Overnight Regulation: Trump to take steps to ban bump stocks | Trump eases rules on insurance sold outside of ObamaCare | FCC to officially rescind net neutrality Thursday | Obama EPA chief: Reg rollback won't stand MORE (R-Ala.), the ranking member of the Budget Committee, last week launched a similar protest against the legislation. He argued budgetary rules prohibit the Senate from taking up appropriations work without first passing a budget. His point-of-order protest was quashed 56-40.

The legislation in question is H.R. 2055, the Military Construction, and Veterans Affairs and Related Agencies appropriations bill. It would increase funding for the VA by 5.8 percent and cut military construction spending by $2.6 billion to reflect anticipated base closures and realignments.