For this fiscal year alone, the deal would add $50 billion in spending, divided equally between defense and domestic programs, as well as $16 billion for emergency war spending, half for the military, half for the State Department. Together, that represents an increase of $66 billion above the spending limits for 2016, not far off the $70 billion increase Mr. Obama requested.

From the moment he introduced his budget Feb. 2, Mr. Obama held firm on his demand that Congress break through the punishing across-the-board cuts known as sequestration in the Budget Control Act to provide equal increases to domestic and military spending. He promised to veto any spending bill that adhered to the statutory spending caps, made good on that threat this month by vetoing a popular defense policy bill, enlisted the support of congressional Democrats with whom his White House had sometimes sparred on budget matters, and capitalized on Republican divisions to get his way.

Senate Democrats created an impenetrable wall for Republicans determined to stick to the caps, filibustering the spending bills that reached the Senate floor and threatening to block the ones that did not. House Democrats stayed in lock step with Mr. Obama as well, with Representative Nancy Pelosi of California, the minority leader, promising that her troops would sustain the president’s veto.

The result was a deal that would raise spending $80 billion, or about 1 percent, over the next two years while enacting an array of cuts that Democrats found palatable. The deal also would suspend the statutory debt limit — on track to be breached on Tuesday without action from Congress — until March 2017, beyond his presidency. It also contains a provision Ms. Pelosi had pressed for to avert large Medicare premium increases for some beneficiaries.