Senators passed the Bulletproof Vest Grant Program Reauthorization by a voice vote.
The presidential hopeful hasn’t ruled out a vote for the measure.
Two House lawmakers have introduced legislation to bolster the federal government's efforts to extradite fugitives who have sought refuge abroad.
Rep. Ron DeSantis's (R-Fla.) bill would not apply to current lawmakers.
The GOP leader made a motion Wednesday to move to "fast-track" legislation.
Martin Matishak 05/06/15 10:45 AM EDT
More than two dozen Republicans are making their case to the Rules Committee.
Senators are expected to debate the legislation ahead of a vote on Thursday.
Ted Cruz was one of just three senators to vote against tabling the veto.
Rand Paul and Ted Cruz opposed, while Marco Rubio and Lindsey Graham voted yes.
Rep. Steve King opposes allowing illegal immigrants to serve in the military.