(CNN) - One of the Gang of Eight senators who negotiated an immigration deal headed to the Senate floor says the bill does not yet have support to overcome a potential filibuster.
"At this moment we have not found 60 votes in the Senate," Sen. Robert Menendez, D-New Jersey, said in an interview on the Spanish-language network Univision that was translated by CNN. "We still need more votes in the chamber."
The immigration legislation passed the Senate Judiciary Committee on Tuesday with support from 10 Democrats and three Republicans, including Sens. Jeff Flake and Lindsey Graham, two other members of the Gang of Eight. After months of backroom crafting by the four Democrats and four Republicans in the informal group, as well as negotiations with labor and other groups, the committee considered some 300 amendments and rejected several which some senators considered poison pills that would doom the bill.
It was important that the committee kept largely intact the product of their negotiations, Menendez said in the interview, but he said much needed to be done before the bill could pass the full Senate, where he indicated debate will likely begin on June 10.
He hoped a significant margin in the Senate would put pressure on the GOP-led House to sign on. A separate bipartisan effort has been under way there and appears to have survived a dispute over how undocumented immigrants' health care costs would be covered.
Members of both parties want to see immigration legislation pass this year, and the effort has the support of President Barack Obama and the Democratic and Republican Senate leaders.
Neither party, however, has enough to overcome a Senate filibuster on their own.
In a statement after the committee vote, Menendez wrote that the legislation faces "a long road and our work is far from done."
As written now, the bill would create a 13-year path to citizenship for many of the 11 million undocumented immigrants in the United States.
Univision said the interview will air Sunday on the network's "Al Punto" program.
– CNN's Deirdre Walsh and Alan Silverleib contributed to this report