The 52-48 overnight vote puts pressure on the GOP-controlled House, which plans to take up its own competing budget resolution next week.

Before adopting Republicans’ budget resolution, senators engaged in an all-night parliamentary marathon that Democrats used to try to force the G.O.P. into politically damaging votes.

Republicans’ budget blueprint cleared the Senate, but a Democratic amendment marathon aimed to put GOP lawmakers on the record regarding potential Medicaid cuts and other politically sensitive issues.