A day after labor and business groups struck a deal on a new guest-worker program, key senators said they are within reach of finalizing an immigration overhaul proposal.

Members of the Senate’s bipartisan “gang of eight,” which is crafting a comprehensive immigration bill, said they have not signed off on a proposal just yet, but are likely to unveil it next week.

“With the agreement between business and labor, every major policy issue has been resolved,” Sen. Charles E. Schumer said Sunday on NBC’s “Meet the Press.”

The New York Democrat, who is a member of the group, said senators have not explicitly agreed to the proposal because the bill’s language has not been fully drafted, but Schumer said he is “very, very optimistic” there will be an agreement next week, when the Senate returns from its spring recess.

“We’ve all agreed that we’re not going to come to a final agreement until we see draft legislative language and we agree on that. We drafted some of it already; the rest of it will be drafted this week,” Schumer said. “And so I am very, very optimistic that we will have an agreement among the eight of us next week.”

Schumer said after a markup by the Judiciary Committee in April, the bill would be on the Senate floor, “God willing, in May.”

The guest-worker program has always been one of the thorniest issues facing lawmakers, having previously helped derail passage of an immigration overhaul in 2007. The deal between the AFL-CIO and the Chamber of Commerce is likely to propel the legislation forward.

“Business and labor have an agreement on the future flow [of foreign workers], which has been the issue that has undone immigration reform in the past,” Schumer said. “So this is a major, major obstacle that’s overcome.”

Under the framework, the number of new guest-worker visas can not be below 20,000 or above 200,000 in any year. The agreement would also require employers to pay guest workers what they typically pay regular workers doing the same job, or the prevailing wage, whichever is higher.

Sen. Lindsey Graham, R-S.C., another member of the working group, confidently predicted that an immigration overhaul would pass both the Democratic Senate and the GOP-controlled House in the coming months.

“I think we’ve got a deal,” he said on CNN’s “State of the Union” on Sunday. “We’ve got to write the legislation, but 2013, I hope, will be the year that we pass bipartisan immigration reform.”

Other members of the bipartisan Senate group were less enthusiastic, but signaled it is only a matter of time before the bill is released.

“We’re much closer with labor and business agreeing on this guest-worker plan. That doesn’t mean we’ve crossed every I or dotted every T, or vice versa,” Sen. Jeff Flake, R-Ariz., said on “Meet the Press.”

“We’ve still got a ways to go in terms of looking at the language and making sure that it’s everything we thought it would be,” Flake added. “But we’re closer, certainly.”

Sen. Marco Rubio, a Florida Republican and member of the bipartisan group, issued a statement Sunday saying he is encouraged by the business-labor agreement and believes the Senate group will soon be able to agree on a legislative proposal.

But reports that the senators have already agreed on a bill are “premature,” Rubio said.

And in a nod to concerns of fellow Republicans, such as Alabama Sen. Jeff Sessions, Rubio underscored his opposition to rapidly moving the bill through the Senate.

“We will need a healthy public debate that includes committee hearings and the opportunity for other senators to improve our legislation with their own amendments,” he said. “In order to succeed, this process cannot be rushed or done in secret.”