A veto-proof majority in the Senate on Wednesday voted to send the annual defense policy bill to the president’s desk, but that won’t deter the White House from stopping the measure in its tracks.

Senators voted 70 to 27 in favor of the conference report on the National Defense Authorization Act (NDAA), which authorizes $612 billion in spending this fiscal year for defense programs. Nearly all Republicans present — except for presidential candidates Sens. Rand Paul (R-Ky.) and Ted Cruz (R-Texas) — voted for the measure and they were joined by 20 Democrats and independent Sen. Angus King of Maine.

Congress stands little chance of overriding the expected veto due to a lack of votes in the House, which adopted the conference report last week but failed to reach the two-thirds threshold needed for a veto override.

The conference report was the result of months of negotiations, during which lawmakers struck many compromises that have earned praise from both sides of the aisle. But Republicans and many Democrats, especially in the House, remain bitterly divided over the measure’s reliance on the use of war funding from the Overseas Contingency Operations account to pay for specific programs as a way of getting around the so-called sequestration budget caps.

As part of a broader budget battle, the White House is pushing for increases in domestic as well as defense spending and does not want to approve any additional funding for the Pentagon until that standoff is resolved.

Republicans urged Democrats to support the measure despite their discomfort with the sequestration issue, arguing that can be ironed out later as part of negotiations over the annual appropriations bills.

“We are authorizing every dollar the president requested,” Senate Armed Services Committee Chairman John McCain (R-Ariz.) said following the vote. “We have supported and tried to work with the administration.”

McCain went on to stress that he and many others also want to see the budget caps imposed by sequestration “repealed, we want to give the military the ability to plan ahead.”

“But we, when given the amount of money the president requested, we authorized that amount of money,” McCain said. “For him to veto what is fundamentally a budget bill, a policy bill, in the name of cost, is inappropriate.”