The Senate approved Republicans’ budget blueprint just after 2:30 a.m. on Saturday to clear the way for passing President Trump’s domestic agenda, after Democrats forced an overnight session to protest the G.O.P. push to deliver what the president has called “one big beautiful bill” of spending and tax cuts.

The 51-to-48 vote, mostly along party lines, was a crucial step in the Republican effort to fast-track budget legislation through Congress and shield it from a filibuster through a process known as reconciliation. Disagreements between Republicans in the House and the Senate about what should be in that bill had paralyzed them for weeks, but they have forged a fragile and complex compromise allowing them to move forward.

Senators Rand Paul of Kentucky and Susan Collins of Maine were the only Republicans who voted to oppose the measure.

The budget blueprint goes next to the House, which must adopt it before lawmakers in both chambers can set to work drafting the legislation laying out the specific tax and spending cuts they want to enact.

“This resolution is the first step toward a final bill to make permanent the tax relief we implemented in 2017 and deliver a transformational investment in our border, national and energy security,” said Senator John Thune of South Dakota, the majority leader, before the vote.

He added later, “Let’s let the voting begin.”