Roadblocks disappearing, the Senate cleared the way Tuesday for a vote giving eager car buyers until Labor Day to cash in on rebates up to $4,500 for trading in their gas-guzzlers for new, higher-mileage models.

Senate Majority Leader Harry Reid declared he had the votes to pass a $2 billion “cash for clunkers” measure already approved by the House. It would replenish the all-but-exhausted $1 billion program and provide rebates for up to a half-million more Americans in the next month.

Despite reservations, Reid’s GOP counterpart, Mitch McConnell of Kentucky, predicted his party would not block a vote and “the matter will be completed.”

“I think the last thing any politician wants to do is cut off the opportunity for somebody who wants to get a rebate to buy a new automobile,” said Transportation Secretary Ray LaHood, a former Republican congressman from Illinois.

Senate passage would send the legislation to the White House for Obama’s signature and guarantee there would be no interruption in the program that has sent buyers streaming into formerly deserted auto showrooms.