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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 DurbinDemocrats turn on Al Franken Minnesota's largest newspaper calls on Franken to resign Democratic senator predicts Franken will resign Thursday MORE (D-Ill.), Robert Menendez (D-N.J.), Lindsey GrahamLindsey Olin GrahamGOP and Dems bitterly divided by immigration We are running out of time to protect Dreamers US trade deficit rises on record imports from China MORE (R-S.C.) and Marco RubioMarco Antonio RubioRyan pledges 'entitlement reform' in 2018 Richard Gere welcomes lawmakers' words of support for Tibet Dem lawmaker gives McConnell's tax reform op-ed a failing grade MORE (R-Fla.).