Updated: 8:30 p.m.

The Senate cleared a procedural hurdle today on legislation considered crucial to winning Democratic support for trade agreements with Colombia, Panama and South Korea, thanks in part to overwhelming support from Republicans.

The GOP ignored opposition to the Trade Adjustment Assistance measure from two prominent conservative advocacy groups, the Club for Growth and Heritage Action for America, which announced earlier in the day that they opposed the legislation.

With 60 votes required to move to the legislation, the final tally came in at 84-8, including close to three dozen Republicans who voted to end a filibuster on the key procedural motion.

President Barack Obama has yet to submit the free-trade agreements to Congress for ratification, in part because of Republican resistance to TAA. But in July, GOP Sens. Roy Blunt (Mo.) and Rob Portman (Ohio) rounded up enough Republican votes to ensure that TAA legislation could overcome a filibuster. Now, in the face of outside opposition from conservatives, that coalition held and was joined by several more Republicans.

Once it clears the Senate, possibly later this week, the TAA measure would then go to the House. It remains unclear whether the needed GOP support will materialize, although some House Republicans have previously signaled their willingness to support the measure.

“We’re eager to see the Senate finish its work quickly this week so that we can move to consider” the free-trade agreements, House Ways and Means Committee spokesman Jim Billimoria said.