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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. 

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