Sen. Lindsey Graham (R-S.C.), a member of the Group of Eight bipartisan immigration reform negotiators, said today he’s hoping the group “can roll something out for public consumption” by next week.

That’s when Congress comes back into session after the Easter break.

Graham said there’s “not really” a rift with Sen. Marco Rubio (R-Fla.) on the legislation.

“The eight of us are trying to put together a legislative proposal that would go through the regular process. It would go to the Judiciary Committee, where I’m a member. It would be amended, debated, changed, and then go to the full Senate and then eventually to the House,” he said on Fox Business. “The legislative proposal we’re working on I think is a starting point of the debate, not the ending point of the debate.”

The senator outlined his two goals as “prevent a third wave 20 years from now, secure your border.”

“You have a right to your own sovereignty. Control who gets a job. Provide abundant labor to employers who can’t find American workers at a competitive wage,” Graham said. “And as to the 11 million, be firm and fair. I think that’s the long-overdue solution to a very hard problem. And if we don’t get it right this time, it will be a decade or more before anybody takes it up.”

Rubio has asked Judiciary Committee Chairman Pat Leahy (D-Vt.) to take the process slow and avoid talk of imminent legislation.

“The idea of a legislative proposal that is bipartisan coming to the Judiciary Committee I hope will happen next week. You got to go through the committee. Then you go to the full floor of the Senate, then to the House,” Graham said. “Everybody in America will get to read the bill. Those who don’t like it can try to kill it. Those who want to change it will have an opportunity.”

Co-chairman of the Congressional Progressive Caucus Rep. Raul Grijalva (D-Ariz.) said Rubio is “a level of concern.”

“And there has been, you know, some expectation that, come next week, that we will have a rollout, we’ll have a piece of legislation and concepts that we can go forward with. Hearings will start in Judiciary, and — and the process — regular order will begin in the Senate. I think that’s very key,” Grijalva said on MSNBC.

“The backtracking and maybe cold feet on the part of Senator Rubio is — is of concern to me. It’s a concern to advocates. He — he is pivotal. And if he withdraws support or starts talking about piecemeal or slowing it down, then — then the fight, I think — then the whole struggle’s going to intensify.”