The Senate's third-ranking Democrat expressed hope Sunday that a bipartisan group he belongs to will come to an agreement on a proposal to revamp the nation's immigration laws by the end of the week.

"I think we're doing very well. I think that we hope that we can have a bipartisan agreement among the eight of us on comprehensive immigration reform by the end of this week," New York Sen. Chuck Schumer said on CBS News's "Face The Nation."

Schumer is part of a bipartisan "Gang of Eight" senators working to develop a broad immigration reform proposal. Following an agreement reached late last month between business and labor leaders over a new guest-worker program, the group had worked out its last major policy issue, Schumer said last weekend. He reiterated that view Sunday.

"Thus far, we are on track. All of us have said that there will be no agreement until the eight of us agree to a big, specific bill. But hopefully we can get that done by the end of the week," Schumer said Sunday.

"By the end of the week?" asked "Face The Nation" host Bob Schieffer.

"Hopefully -- that's what we're on track to do," responded Schumer.

Sen. Marco Rubio (R-Fla.), another key member of the group, said last week that "reports that the bipartisan group of eight senators has agreed on a legislative proposal are premature."

Sen. Lindsey Graham (R-S.C.), another member of the group, said Sunday that he was hopeful a deal could be reached "in the next couple of weeks," and that the group is "revisiting" the guest-worker agreement between business and labor.

"It's the guest worker program. High-skill and low-skill labor:  How can you access it in an affordable fashion when you can't find an American worker," Graham said on NBC News's "Meet The Press."

Graham said Rubio will offer his support if Democrats embrace a "merit-based immigration system" in addition to a guest-worker program.

"He will be there only if the Democrats will embrace a guest-worker program and a merit-based immigration system to replace the broken one, and we'll regain our sovereignty by securing our borders and having control of jobs through E-Verify," Graham said. "Marco will be there. If we get the 11 million right on our side, it puts pressure on the Democrats to come up with a practical guest-worker program."

When asked whether he thinks Rubio will ultimately sign off on an agreement, group member Sen. John McCain (R-Ariz.) didn't provide a yes or no answer, instead praising the Florida Republican's input.

"He's been very helpful and important in this whole effort that we've been making. He's reached out to conservative sides, including talk show hosts and others. Marco has been very important," McCain said on "Face The Nation."