But opponents of repeal, including Senator John McCain of Arizona, the senior Republican on the Armed Services Committee, blocked debate on the measure.
Lawmakers issued news releases and boasted about their efforts to block debate on the gun bill despite some popular provisions.
The Senate voted last week to consider the fast-track measure, two days after Democrats had blocked debate on the bill, which would clear the way for a 12-nation Pacific trade agreement.
But Senate Republicans voted unanimously to block debate on the bill, the annual authorization of military programs, after the majority leader, Harry Reid, Democrat of Nevada, said he would attach a number of the Democrats' election-year priorities to it while also moving to limit the amendments offered by Republicans.
After two successful efforts to block debate on the Democrat's proposal, the Republicans have agreed to let the bill move to the floor of the Senate.
"A great number of our colleagues abandoned positions that they had held very clearly and very publicly for a long time," said Sen. Sheldon Whitehouse (D-R.I ., who was joineD-R.I .n. Jeff Merkley (D-Ore). at a press conference to announce next steps after Republican senators blocked debate on the bill Monday, and then again on Tuesday.
A Republican filibuster aimed at blocking debate on proposed gun measures is expected to be thwarted Thursday.
Republicans have voted to block debate on bills scores of times over the last few years.
After Republicans blocked debate on both measures by denying Democrats the 60 votes needed to move forward, Senator Harry Reid of Nevada, the majority leader, did not try to disguise what was shaping the oil and economic fights on Capitol Hill.
