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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 DurbinLive coverage: FBI chief, Justice IG testify on critical report Hugh Hewitt to Trump: 'It is 100 percent wrong to separate border-crossing families' Opioid treatment plans must include a trauma-informed approach MORE (D-Ill.), Robert Menendez (D-N.J.), Lindsey GrahamLindsey Olin GrahamOvernight Health Care — Presented by the Association of American Medical Colleges — Trump officials move to expand non-ObamaCare health plans | 'Zero tolerance' policy stirs fears in health community | New ObamaCare repeal plan McCain, Coons: Trump should withdraw controversial refugee nominee GOP senators drafting legislation to keep immigrant families together MORE (R-S.C.) and Marco RubioMarco Antonio RubioDem scores upset over Republican in Florida county commissioner race GOP senators introduce bill to prevent family separations at border McCain, Coons: Trump should withdraw controversial refugee nominee MORE (R-Fla.).