BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery MORE has said repeated that the House would likely consider the Senate-passed bill, S. 1813, once it passes. The Senate bill is a two-year, $109 billion authorization bill, which is seen as more palatable to many Republicans than the original GOP bill that was floated, a $260 billion, five-year authorization.

Reid said the Senate bill would "save or create" 2.8 million jobs, and that its approval would have an immediate jobs impact, since current highway authorization expires at the end of March.

"At the end of this month, the highway bill expires," he said. "That could lead to the laying-off, termination of well more than 1 million people."

Reid said the Senate would need just two more amendment votes on Wednesday, and would then move to a final passage vote. Votes on the highway bill are still scheduled to start at 11:30 a.m.

Reid also repeated that there could be up to 17 cloture votes on district court judge nominees today, and indicated the Senate is closer to moving a House-passed capital formation bill, the Jumpstart Our Business Startups (JOBS) Act, H.R. 3606.

"I think there's general agreement there should be an extremely limited number of amendments, and move this as quickly as possible," Reid said.