Reid has been urging swift passage of the legislation, which lets the FDA charge drug companies user fees when they submit their brand name drugs for approval.

Earlier on Monday Reid said he was "cautiously optimistic" about the legislation's likely passage. He, as well as, Sens. Mike EnziMichael (Mike) Bradley EnziThis week: Congress gets ball rolling on tax reform How the effort to replace ObamaCare failed Senate GOP budget paves way for .5T in tax cuts MORE (R-Wyo.) and Tom HarkinTom HarkinThe Hill's 12:30 Report Distance education: Tumultuous today and yesterday Grassley challenger no stranger to defying odds MORE (D-Iowa), the cosponsors of the bill, have said they hope the bill does not change too much going forward given the bipartisan support it has in its current form.

"I'm cautiously optimistic that the spirit of bipartisanship will continue because Democrats can't pass this legislation without the cooperation of our Republican colleagues," Reid said.

Later on Monday Harkin said he expected the Senate to vote on amendments to the legislation as the chamber has with other recent bills. Harkin said he hopes those amendments would be relevant to the FDA bill.

"I would say neither Democrats nor Republicans got everything they wanted in this bill," Harkin said. "We would expect that all of these amendments would be relevant to the bill."