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 KingMcConnell on filibuster talk: Democrats want to 'vandalize' Senate rules Manchin draws line against repealing legislative filibuster Filibuster reform gains steam with Democrats 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 Mason ReidMcConnell warns Democrats not to change filibuster rule Filibuster reform gains steam with Democrats The Hill's Morning Report - Trump wants executive order on policing; silent on pending bills 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 CruzRafael (Ted) Edward CruzTrump administration grants funding extension for Texas testing sites Hillicon Valley: Democrats introduce bill banning federal government use of facial recognition tech | House lawmakers roll out legislation to establish national cyber director | Top federal IT official to step down GOP lawmakers join social media app billed as alternative to Big Tech MORE (Texas) and Rand PaulRandal (Rand) Howard PaulGOP Arizona lawmaker says Fauci and Birx 'undermine' Trump's coronavirus response Fauci: 'We are not going in the right direction' FBI says Breonna Taylor case is 'top priority' for Louisville agents MORE (Ky.), who are both running for president, were the only Republicans to vote against the bill. Two other 2016 candidates, Sens. Lindsey GrahamLindsey Olin GrahamHillicon Valley: Senate panel advances bill targeting online child sexual abuse | Trump administration awards tech group contract to build 'virtual' wall | Advocacy groups urge Congress to ban facial recognition technologies Senate panel advances bill targeting online child sexual abuse The Hill's Campaign Report: The political heavyweights in Tuesday's primary fights MORE (S.C.) and Marco RubioMarco Antonio RubioTrump administration eyes new strategy on COVID-19 tests ACLU calls on Congress to approve COVID-19 testing for immigrants Republicans fear backlash over Trump's threatened veto on Confederate names 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 KaineTimothy (Tim) Michael KaineOvernight Defense: Lawmakers demand answers on reported Russian bounties for US troops deaths in Afghanistan | Defense bill amendments target Germany withdrawal, Pentagon program giving weapons to police Senators aim to limit Trump's ability to remove troops from Germany Filibuster reform gains steam with Democrats 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 Sidney McCainJuan Williams: Time for boldness from Biden Democrats lead in three battleground Senate races: poll Republican Scott Taylor wins Virginia primary, to face Elaine Luria in rematch 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 McConnellAddison (Mitch) Mitchell McConnell'Comrade' Trump gets 'endorsement' from Putin in new mock ad by Lincoln Project ACLU calls on Congress to approve COVID-19 testing for immigrants Carville repeats prediction that Trump will drop out of race 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 DurbinRichard (Dick) Joseph DurbinHillicon Valley: Facebook takes down 'boogaloo' network after pressure | Election security measure pulled from Senate bill | FCC officially designating Huawei, ZTE as threats Overnight Defense: Democrats blast Trump handling of Russian bounty intel | Pentagon leaders set for House hearing July 9 | Trump moves forward with plan for Germany drawdown Democrats, voting rights groups pressure Senate to approve mail-in voting resources 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.