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.

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.

The hours-long “vote-a-rama” rambled along in a dreaded but crucial part of the budget process, as senators considered one amendment after another, largely from Democrats trying to halt it.