Schumer spoke on CBS' "Face the Nation" alongside Sen. John McCain, R-Ariz., another leader of the immigration talks, who suggested there could be a tough road ahead for the contentious legislation.
"There will be a great deal of unhappiness about this proposal because everybody didn't get what they wanted," McCain said. "There are entrenched positions on both sides of this issue as far as business and labor."
A deal on immigration is a top second-term priority for President Barack Obama, and his senior adviser Dan Pfeiffer said Sunday that the bill being developed in the Senate is completely consistent Obama's approach -- even though the Senate plan would tie border security to a path to citizenship in a manner Obama administration officials have criticized.
Pfeiffer didn't answer directly when asked on "Fox News Sunday" whether Obama would sign legislation making a path to citizenship contingent on first securing the border, as negotiators in the Senate are doing. But he suggested Obama was supportive of the Senate plan.
"What they are looking at and what has been talked about in the Gang of Eight proposal is 100 percent consistent with what the president is doing so we feel very good about it," Pfeiffer said. "And they are looking at it in the right way."
Obama has stressed that a path to citizenship should not have major hurdles in front of it, and some immigration advocates believe that's what a requirement for a secure border would amount to. Obama's Homeland Security secretary, Janet Napolitano, has rejected the argument that border security must be achieved before a comprehensive immigration package or any pathway to legalized status can be done.
But Republicans involved in the Senate negotiations have made clear that border security is a must for them before those living here illegally can be allowed to move toward citizenship.
"We are going to secure that border and it will be tied to a pathway to citizenship or there will be no deal," Sen. Lindsey Graham, R-S.C., another negotiator on the bill, said Sunday.
Graham also suggested that disagreement over a new low-skilled worker program could still be hanging up an overall immigration deal -- even after an agreement a week ago between the AFL-CIO and the U.S. Chamber of Commerce.
The hard-won deal between labor and business would ultimately allow up to 200,000 workers a year into the U.S. to fill jobs in construction, hospitality, nursing homes and other areas where employers now say they have a difficult time hiring Americans or legally bringing in foreign workers. Even after the deal was struck, some industries, such as construction, continued to voice complaints about the terms.
Without offering details, Graham said on NBC's "Meet the Press" that negotiators were revisiting the low-skilled worker deal. But he issued a statement a short time later saying he was confident the agreement would hold.
Graham sounded optimistic overall, predicting the bill would pass the 100-member Senate with 70 votes in favor. Senators believe an overwhelming bipartisan vote is needed in the Democratic-led Senate to ensure a chance of success in the Republican-controlled House. Floor action could start in the Senate in May, Schumer said.
Meanwhile two lawmakers involved in writing a bipartisan immigration bill in the House, Reps. Luis Gutierrez, D-Ill., and Mario Diaz-Balart, R-Fla., sounded optimistic that they, too, would have a deal soon that could be reconciled with the Senate agreement.
"I am very, very optimistic that the House of Representatives is going to have a plan that is going to be able to go to a conference with the Senate in which we're going to be able to resolve this," Gutierrez said Sunday on CNN's "State of the Union".