Annual defense policy legislation could be headed to the White House as soon as Wednesday after the Senate voted to cut off debate on the measure, even as the chamber’s top Democrat pledged his caucus would vote to sustain a promised presidential veto.

Senators voted 73-26 Tuesday to invoke cloture on the conference report for the fiscal 2016 defense authorization bill (HR 1735), which sets national defense policy and sets funding levels for Pentagon programs. Twenty-one Democrats joined all but one Republican — Rand Paul — in ending debate on the measure. The bill is subject to 30 hours of post-cloture debate, unless senators reach an agreement to move up the vote or push it back. The only senator not to vote was Florida Republican Marco Rubio.

Democrats did not put up a fight to filibuster the measure, which the White House has said President Barack Obama will veto, in part over its inclusion of tens of billions of dollars in additional war-related funds to supplement the everyday operations of the Pentagon and evade the sequestration-level spending caps for national defense. Tuesday’s vote, though only a procedural vote, was a veto-proof majority.

As Armed Services conferees rolled out the final legislation last week, Republicans warned the White House against vetoing the must-pass bill, citing the key pay and benefit components in the legislation and the unstable global security situation. Senate Majority Leader Mitch McConnell, R-Ky., warned Democrats who supported cloture and passage of the bill in June not to change their votes.

“This is not the time to flip-flop on the men and women who protect us,” McConnell cautioned. “This is not the time to flip-flop on America’s defense, certainly not in this age of daunting global threats.”

On the floor Tuesday, Senate Minority Leader Harry Reid, D-Nev., responded that, in his caucus, “not all of them will vote the same way they did last time” on the defense bill, but vowed they would produce enough votes to uphold Obama’s veto, which could be overturned with 67 votes.

“My Democrats, our Democrats, have stated without any question, if it comes time that we sustain a presidential veto, that will be done,” Reid said.

While cloture was invoked with sizable Democratic support — and a veto-proof majority — it is unclear how many of those senators will support final passage of the legislation. The Senate’s version of the bill passed in June with 71 votes, including 22 Democrats, which would have been a large enough majority to override a presidential veto. But only two Democrats, Tim Kaine of Virginia and Joe Donnelly of Indiana, signed the conference report.

Senate Armed Services Chairman John McCain, R-Ariz., piled on, highlighting the “tens if not hundreds” of provisions that support military service members, calling opposition the legislation over the war funding issue “a disgrace.”

“There has never been, in my view, a greater need to authorize and fund our military, which is facing more challenges than since the end of World War Two, than today,” McCain said.

“On an overall, not a specific issue, but a broad issue of the budget, my friends want to turn down our authorization and our responsibilities to the men and women who are serving in the military,” he added.

The House passed the measure last week by a 270-156 vote, falling short of the 290 needed to enact the bill without the president’s signature.

The bill would authorize a topline of $612 billion in national defense spending, including a $496.4 billion Defense Department base budget. The measure also would authorize $18.6 billion for national security programs within the Energy Department as well as $7.6 billion in mandatory spending. It contains a further $89.2 billion in Overseas Contingency Operations funds, $38.3 billion above the president’s request. The contingency fund is not capped by law.