Sen. Robert Menendez, D-N.J., said Friday there were currently not enough votes in the Senate to pass the measure, even though it passed through the Senate Judiciary Committee Friday by a 15-3 vote.
"We don't currently have 60 votes identified in the Senate," Menendez told the Spanish-language television network Univision. "We need to add more votes on the floor."
Menendez urged supporters of immigration reform to contact their U.S. senators to urge passage of the bill.
The Hill said proponents were hoping to pass the bill with at least 70 votes to improve its chances in the Republican-controlled House of Representatives.
Menendez said he was optimistic further negotiations in the Senate would bring in the 60 votes needed to pass the bill between June 10, when Congress reconvenes, and the July Fourth holiday, when it goes into recess again.
"I believe that in those three weeks we can get the necessary votes and we will have the community," Menendez said. "We are expecting that and working for that."