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 $340 billion budget framework is a step toward unleashing money the Trump administration says it needs for mass deportations and border security.