"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 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 RyanMcConnell names Senate GOP tax conferees House Republican: 'I worry about both sides' of the aisle on DACA Overnight Health Care: 3.6M signed up for ObamaCare in first month | Ryan pledges 'entitlement reform' next year | Dems push for more money to fight opioids 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 SessionsGOP strategist donates to Alabama Democrat House passes concealed carry gun bill Rosenstein to testify before House Judiciary Committee next week 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.