The bill will be placed on the Senate's calendar without going through the committee process.
The Senate Majority leader plans a series of votes for Wednesday.
The Senate could take a procedural vote Thursday on the attorney general nominee.
Lawmakers are "not close to a consensus" on action against ISIS.
The Arizona Republican said that if Republicans don't address immigration "we do not win the 2016 election."
Sen. Ben Cardin said Republicans have "a lot of interest" in putting forward amendments.
"It is time to put our money where our mouths are, literally," Rep. Luis Gutiérrez said.
Kevin Cirilli 04/21/15 04:06 PM EDT
The Chamber of Commerce hopes to convince more Republicans to back the bank.
The House sent long-stalled legislation to the president's desk on Tuesday to improve energy efficiency in buildings.
But, Sen. Amy Klobuchar said work remains to be done.