"I feel we'll have a good, strong showing from the Democratic side. But we need bipartisan support to pass it," he said Sunday on CBS' "Face the Nation."
Durbin said he spoke to some Republicans, who are wary of voting for the bill due to the upcoming 2016 presidency race and pressure from the Tea Party in this coming year's re-election.
Seven out of the 12 Republican senators running for re-election are facing opposition from Tea Party members in the primaries, Durbin noted.
"Remember, Boehner faced them down before this vote in the House and finally said, 'We've got to do something here. We can't let a handful of members really dictate what happens in the House and what happens to our future.' I think he learned his lesson from that government showdown. I hope the Republican senators heard the same message."
Republican Sen. John McCain was also on "Face the Nation" Sunday and said he will support the bill.
"I think it's important that we have this agreement. As you know, I'm particularly sensitive about the military. I've talked to our military leaders they say they badly need this relief," he said.