Congress is poised to approve the annual defense policy bill after it cleared a key procedural test on Tuesday in the Senate, but a veto fight with President Obama still looms.

The Senate voted 73 to 26 to begin considering the bill, enough support to avoid any potential filibusters of the deal put together by House and Senate negotiators.

But a bigger fight lies ahead.

President Obama has promised to veto the legislation over its use of extra war funding in the Overseas Contingency Operation (OCO) account to pay for certain programs.

Republican leaders say the OCO funds are necessary to get around so-called sequestration spending caps, but Democrats and the White House want to see Congress lift those spending caps for domestic programs as well, not just find a workaround to give defense spending a special break.

After Tuesday’s vote, it appears the Senate could collect enough votes to override a veto — more senators voted for the conference report on the National Defense Authorization Act than had voted for the initial Senate version earlier this spring. although though one more senator also voted no.

The House, however, does not appear to have the votes to override a veto. Last week, it voted 270-156 in favor of the conference report, 20 votes shy of a veto-proof majority.