"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 DurbinDick DurbinLobbying World Judiciary Dems seek hearing on voting rights Elizabeth Warren stumps, raises funds for Duckworth MORE (D-Ill.), Robert
Menendez (D-N.J.), Lindsey GrahamLindsey GrahamNever Trump voices face tough decision Trump: GOP critics can come back after my 'two terms' Graham: GOP has 'lost its way' on Trump MORE (R-S.C.) and Marco RubioMarco RubioFlorida's GOP governor urges Congress to approve Zika funding Shellshocked GOP donors give Trump a second look Never Trump voices face tough decision MORE (R-Fla.).