The Senate will vote to extend the popular “cash-for-clunkers” program before going home on Friday, Majority Leader Harry Reid declared Tuesday in a strong signal the government won’t let the trade-in rebates die under the surging demand that has almost exhausted federal backing.

Reid’s GOP counterpart, Mitch McConnell of Kentucky, predicted his party would not block a vote and “the matter will be completed.” But Republicans’ acquiescence depended on whether Reid would allow them to try to make changes to the House-passed version of the bill — and that could slow down the legislation anew.

“We’ll pass cash for clunkers before we leave here,” Reid told reporters after Democrats lunched at the White House with President Barack Obama, who has pushed hard for the Senate to add $2 billion to the program.