By Jean-Paul Salamanca (staff@latinospost.com) | First Posted: Apr 01, 2013 11:29 AM EDT

The long-awaited push to fix the nation's immigration laws looks like it might be ready to reach Congress for a vote soon.

The bipartisan U.S. Senate panel working on a comprehensive immigration reform bill said Sunday that business and labor groups have reached an agreement on a guest worker program, which has resolved all of the major outstanding issues in the move to create a bill reforming the nation's immigration laws.

Sen. Lindsey Graham, R-S.C., a member of the panel, told CNN's "State of the Union with Candy Crowley" Sunday that the panel will be unveiling their agreement next week. The bill is expected to include a pathway to citizenship for millions of undocumented immigrants living in U.S. borders as well as stronger border security and, now, ways for businesses to hire low- and high-skilled labor coming in from abroad.

"Conceptually, we have an agreement... It will be rolled out next week. Yes, I believe it will pass the House..." Graham said Sunday.

Sen. Charles Schumer, D-N.Y.., also told NBC's "Meet the Press" the same say that he felt there would be "extensive markup and debate on the bill in April" and that it could get to the Senate floor, "God willing, in May."

"I am very, very optimistic that we will have an agreement among the eight of us next week," Schumer said, adding that he felt "we're on the right track."

His comments were echoed by fellow "Gang of Eight" member Sen. Jeff Flake, R-Ariz., who also appeared on "Meet the Press."

"We're committed to this if we can get the language right," he said.

The remarks came barely a day after the AFL-CIO and the U.S. Chamber of Commerce announced their agreement Saturday regarding a guest worker program for low-skilled workers. Previously, there was a dispute between the two sides over how much immigrant workers in the program would be paid, the AFL-CIO pushing for higher wagers than the chamber was willing to agree to.

In contrast to remarks by key members of the panel working to create a new immigration bill, Sen. Marco Rubio, R-Fla., made some scaled-back comments on Sunday, stating that there was "substantial progress" made on a bill, but there was still work to be done before a finalized bill could be put forward.

"We have made substantial progress, and I believe we will be able to agree on a legislative proposal that modernizes our legal immigration system, improves border security and enforcement and allows those here illegally to earn the chance to one day apply for permanent residency contingent upon certain triggers being met. However, that legislation will only be a starting point," Rubio said in a statement through his office.

Rubio added that there is still a need for "healthy public debate" including committee hearings and a chance for other senators outside the group to add in amendments to the bill.

Rubio also stressed the importance of not rushing the bill, adding that the finalized version of the bill "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."

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