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Schumer on Thursday said the Gang is "very close to an agreement."

"We expect to meet our goal of having comprehensive immigration reform supported by all eight of us by the end of March. We’re on track," Schumer said.

But McCain on Monday cautioned that the negotiations were continuing, and wouldn't guarantee a deal by early April.

"I can't guarantee anything," McCain said at a town hall in Arizona. “We're still in serious negotiations, but we have made progress. We are negotiating now, as we are in recess."

President Obama, who has urged Congress to pass a comprehensive immigration reform plan early in 2013, on Monday said he expects Congress to debate a "comprehensive, sensible" reform plan in April. 

The other members of the Gang of Eight are Sens. Dick DurbinRichard (Dick) Joseph DurbinAmerica’s waning commitment to the promise of the First Amendment Senate rejects Trump immigration plan What to watch for in the Senate immigration votes MORE (D-Ill.), Robert Menendez (D-N.J.), Lindsey GrahamLindsey Olin GrahamCongress punts fight over Dreamers to March Pence tours Rio Grande between US and Mexico GOP looks for Plan B after failure of immigration measures MORE (R-S.C.) and Marco RubioMarco Antonio RubioColbert: Students taking action on gun violence 'give me hope' Lawmakers feel pressure on guns Florida lawmaker's aide fired after claiming shooting survivors were 'actors' MORE (R-Fla.).