(CNN) - Members of the bipartisan Gang of Eight senators working out immigration overhaul legislation said Sunday they expect to have a draft bill agreeable to their circle by the end of this week. But Sen. Marco Rubio, R-Florida, a member of the group, issued a statement saying it was too soon to consider the deal struck.
"I'm encouraged by reports of an agreement between business groups and unions on the issue of guest workers. However, reports that the bipartisan group of eight senators have agreed on a legislative proposal are premature," he wrote.
Shortly after that statement was released, Sen. Lindsey Graham, R-South Carolina, signaled on CNN's "State of the Union with Candy Crowley" that the deal will be reached within days.
"It's got to be written up. We haven't signed off," he said. "There are a few details yet, but conceptual - we have an agreement between business and labor, between ourselves. It has to be drafted. It will be rolled out next week."
Sen. Chuck Schumer, D-New York, concurred on the timeline and but acknowledged a few issues remained to be settled.
"As Sen. Rubio correctly says, we have said we will not come to final agreement until we look at all of the legislative language, and he's correctly pointing out that that language hasn't been fully drafted. There will be little kerfuffles, but I don't think any of us expect there to be problems," he said on NBC's "Meet the Press."
Sen. Jeff Flake, R-Arizona, also sounded optimistic a deal would be reached but said on NBC, "We've still got a ways to go with the language."
Both Schumer and Rubio are seen as particularly important in this process, with Schumer the Democratic deal-maker who is bringing the sides together and Rubio key to bringing on board conservative members of both the House and Senate.
Schumer said any difference between his view and Rubio's view of progress toward a deal is just "semantics."
"I don't think he'll walk away," Schumer said when asked, adding, "He's had a lot of input into the bill. Obviously his views are not the same as the other seven of us. Every one of us has different views. ... He is protecting some of the things that he thinks are very important in the bill, but I don't think that will stand in the way in any way of any agreement."
On Saturday, leaders of labor and business groups reached consensus on the outlines of a guest worker program - a sticking point in the area of immigration between influential lobbies including the AFL-CIO and Chamber of Commerce - a source familiar with those talks told CNN.
The consent of business and labor groups is important not only because it means neither side will fight the bill, but also because a key goal of the Gang of Eight is to restructure the current system for allocating U.S. visas. Graham said on CNN that the Gang of Eight would propose legislation that prioritizes visas for business purposes over visas for family members, as well as preventing a future wave of illegal immigration once the path to citizenship is implemented for those currently undocumented and in the U.S.
Schumer said with those groups in agreement, "every major policy issue has been resolved on the Gang of Eight," meaning a deal would emerge this week, followed by "extensive markup and debate on the bill in April (in the Senate Judiciary Committee) and then we go to the floor, God willing, in May. I think we're on track."
After a series of legislative backroom deals on fiscal matters, Rubio underlined with his statement the importance of bringing this deal through what members call "regular order," the process of amending draft legislation in committee, on the floor, and eventually a meeting of the two houses to reconcile any differences.
"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," Rubio wrote. "Eight senators from seven states have worked on this bill to serve as a starting point for discussion about fixing our broken immigration system. But arriving at a final product will require it to be properly submitted for the American people's consideration, through the other 92 senators from 43 states that weren't part of this initial drafting process.
"In order to succeed, this process cannot be rushed or done in secret," he wrote.
In addition to Rubio, Graham, Schumer and Flake, the Gang of Eight includes Sens. Michael Bennet, D-Colorado; Dick Durbin, D-Illinois; John McCain, R-Arizona; and Robert Menendez, D-New Jersey.
President Barack Obama has described immigration as a top priority of his, but appears to have left the negotiating largely up to Capitol Hill, especially after a draft administration plan for immigration reform was reported publicly and drew criticism from Republicans, including Rubio.
A White House official said Saturday the president "continues to be encouraged by progress being made by the bipartisan group of senators."
"We look forward to seeing language once it is introduced, and expect legislation to move forward as soon as possible," the official said.
- CNN's Kevin Liptak, Jessica Yellin and Kevin Bohn contributed to this report
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