Republican senators pushed a $340 billion budget framework to passage early Friday, chugging through an all-night session and Democratic opposition in a step toward unleashing money the Trump administration says it needs for mass deportations and border security that top their agenda.

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

Democrats have planned a tranche of amendments that challenge or limit the authority of Musk, the billionaire adviser to Donald Trump.