Sen. Marco RubioMarco RubioRepublicans giving Univision the cold shoulder: report Week ahead: Senate panel to vote on Trump's Labor pick Senators introduce new Iran sanctions MORE (R-Fla.) on Sunday cautioned that reports that a bipartisan group in the Senate was close to a deal on reforming the nation’s immigration laws was “premature.”

“I’m encouraged by reports of an agreement between business groups and unions on the issue of guest workers,” said Rubio in a statement released Sunday. “However, reports that the bipartisan group of eight senators have agreed on a legislative proposal are premature.”

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Rubio’s statement came after reports Saturday said business and labor groups had reached a deal on a plan to grant visas to low-skilled guest workers, a key stumbling block in congressional efforts to forge immigration reform.

The news led to speculation that the “Gang of Eight” senators who are working on an immigration reform deal were nearing a final accord. 

Rubio’s colleagues in the group were much more optimistic about quickly finalizing a deal. 

On the Sunday morning shows, Sen. Lindsey GrahamLindsey GrahamOvernight Finance: Dems seek probe of acting SEC chief | Defense hawks say they won't back short-term funding | Senate seen as start point for Trump infrastructure plan | Dems want more money for IRS Overnight Defense: Pentagon considers more troops for Afghanistan | McCain, Graham won't back short-term funding | GOP defends Trump rules of engagement McCain and Graham: We won't back short-term government funding bill MORE (R-S.C.) said the group had reached a deal “conceptually” and could roll out a bill as early as “next week.” Sen. Charles SchumerCharles SchumerSenate seen as starting point for Trump’s infrastructure plan Dems wait for GOP olive branch after ObamaCare debacle How Obama's White House weaponized media against Trump MORE (D-N.Y.), who helped broker the business-labor agreement, said a floor vote could come as early as May.

Rubio, however, said the group had made “substantial progress” but cautioned that unveiling the legislation would “only be a starting point.”

“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,” said Rubio.

On Saturday, in a letter to Senate Judiciary Chairman Patrick LeahyPatrick LeahySenate braces for fallout over Supreme Court fight Register of copyrights should be presidential appointee GOP senator on going nuclear: 'I really hope that it doesn't come to that' MORE (D-Vt.) Rubio cautioned against a “rush to legislate” on immigration reform. 

He warned that moving too quickly could cost public support for immigration reform. 

“A rush to legislate, without fully considering all views and input from all senators, would be fatal to the effort of earning the public’s confidence,” said Rubio.

Rubio, a Tea Party favorite, would play a key role in winning support for any immigration bill among conservative GOP lawmakers. 

The Senate proposal being finalized will include a pathway to citizenship for illegal immigrants already in the country, heightened border security requirements and efforts to boost both low-skilled and high-skilled labor.