Senate Democrats on Wednesday joined with Republicans to approve an annual defense bill, defying a veto threat from President Obama.

The Senate voted 70-27 in favor of the $612 billion National Defense Authorization Act (NDAA), a wide-ranging measure that would set policy and spending priorities for the Pentagon. Twenty Democrats voted yes, as did Sen. Angus KingAngus KingAngus King: Trump's not draining swamp, he's adding alligators Overnight Cybersecurity: Last-ditch effort to stop expanded hacking powers fails Intel Dems push for info on Russia and election be declassified MORE (Maine), an Independent who caucuses with Democrats.

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While the vote total would be enough for Republicans to override Obama’s promised veto, Democratic leaders insist that some of their members would vote differently if asked to override the president.

“The president is going to veto this. Everyone knows this,” Senate Minority Leader Harry ReidHarry ReidDemocrats local party problem Trump flirts with Dems for Cabinet Lawmakers eye early exit from Washington MORE (D-Nev.) said ahead of the vote. “The House, if they are called upon first to sustain the veto, they will do it. If we’re called up on first to sustain the veto, we will do it.”

Republican Sens. Ted CruzTed CruzLewandowski: Top Cruz aide advised Trump team before NH primary Five reasons why Donald Trump could be the 'Greatest Communicator' Victims of Nazi Art theft need Congress to HEAR MORE (Texas) and Rand PaulRand PaulGOP rep: Trump has 'extra-constitutional' view of presidency The ignored question: What does the future Republican Party look like? Rand Paul skeptical about Romney as secretary of State MORE (Ky.), who are both running for president, were the only Republicans to vote against the bill. Two other 2016 candidates, Sens. Lindsey GrahamLindsey GrahamPentagon should have a civilian chief to give peace a chance Lawmakers eye early exit from Washington Senate passes college anti-Semitism bill MORE (S.C.) and Marco RubioMarco RubioThe ignored question: What does the future Republican Party look like? Graham to roll out extension of Obama immigration program Trump and Cuba: A murky future MORE (Fla.), didn't vote.

The policy bill has been pulled into the larger battle over the GOP’s budget plan, which would appropriate $38 billion to the Pentagon through a war fund account.

Democrats and the White House say the war fund should not be used to skirt congressional budget caps and are demanding that Republicans negotiate a deal to raise spending across the federal government.

But Republicans, and even some Democrats, have questioned why Obama is poised to veto the NDAA, as the bill authorizes spending without actually appropriating the money.

"You know, I started to have conversation with the White House when we were taking this up in committee, telling them their veto threat was a mistake," said Sen. Tim KaineTim KaineTerry McAuliffe: Clinton likely done with politics Becerra leaving Congress to become Calif. attorney general Kaine: 'We have to be at the table’ for recounts MORE (D-Va.), who voted in favor of the NDAA on Wednesday.

"To basically say you'll veto over the [war fund] issue, when we have language in the bill that basically says we should fix the budget caps, I said, 'I think you're drawing the line in the battle at the wrong place.' "

The policy bill has passed Congress for 53 consecutive years, and is typically considered one of the most important legislative tasks for Congress.

Sen. John McCainJohn McCainPentagon should have a civilian chief to give peace a chance McCain to support waiver for Mattis, Trump team says Senators crafting bill to limit deportations under Trump MORE (R-Ariz.), the chairman of the Senate Armed Services Committee, said an Obama veto of the defense bill would be “shameful.”

“If the president vetoes the NDAA, at this time of mounting global threats, he will be prioritizing politics and process over the security of our nation and the well-being of our armed forces.”

Majority Leader Mitch McConnellMitch McConnellTrump flirts with Dems for Cabinet Lawmakers eye early exit from Washington Confirm Scott Palk for the Western District of Oklahoma MORE (R-Ky.) echoed that criticism Wednesday.

“If he does [veto the bill], it will be the latest sorry chapter in a failed foreign policy based on campaign promises rather than policies to realistically meet the threats before us,” he said.

Obama has threatened to veto the policy bill six times before, primarily due to objections on the transfer of prisoners from the Guantánamo Bay prison facility, but never followed through.

But this year will be different, the administration says, due to the president's strong objections to the use of the war fund.

Press secretary Josh Earnest this week called the GOP plan an “irresponsible way to fund our national defense priorities” and reiterated that Obama would reject it.

Rep. Mac Thornberry (R-Texas), the chairman of the House Armed Services Committee, suggested that if Obama vetoes the bill, it would be different from the four times the NDAA has been vetoed in the past 53 years.

"Every one of them were because of something that was in the bill, not because of something that was outside bill, which is thing the president is complaining about today," he said.

If and when Obama’s veto comes, Republicans are likely to try for an override, though success appears unlikely. The House fell short of the two-thirds majority needed to override a veto when it voted on the NDAA last week. And Sen. Dick DurbinDick DurbinLawmakers eye early exit from Washington Senators crafting bill to limit deportations under Trump Warren pushes Dems to get tough with Trump MORE (D-Ill.) warned on Tuesday that Republicans should not assume that Senate Democrats voting for the NDAA would also vote to overturn Obama’s veto.

"If we can't override [a veto] ... outside events will dictate the future and the fate of the legislation," McCain said. "We need 67 in the Senate. It will be very interesting to see how many we hold."

Some military groups have warned Obama against holding the policy bill hostage to the larger funding fight. 

The Military Officers Association of America (MOAA) and the Reserve Officers Association have both sent letters to the president urging him to support the NDAA.

MOAA President Norbert Ryan Jr. said while the concerns about the extra war funding are “legitimate,” the policy legislation “is vital to fulfilling wartime requirements.”

— This story was updated at 5:19 p.m.