Republicans in the group have insisted that the border security requirements be "real" and effective.
"I will not be supporting any law that does not ensure that the enforcement things happen," Sen. Marco Rubio (R-Fla.), a member of the group, told conservative blogger Ed Morrissey on his web radio show.
The "Gang of Eight" must also navigate tricky political waters on immigration, which has long been a contentious issue on Capitol Hill. Schumer conceded that the group does not yet have the support of "every single Democrat" in the Senate, which could make passing a bill more difficult since Republicans have traditionally been less supportive of comprehensive immigration reform.
But Durbin expressed confidence that the handful of holdouts would come around.
"I think you may be pleasantly surprised. At least one of them has come up to me and said, 'I'm open this time,'" Durbin told reporters, but declined to name the senator.
Proponents of immigration reform also face a tougher task in the House of Representatives, which is controlled by Republicans. But Schumer said that his group has talked to a counterpart group of lawmakers in the House working on a bill as well as the Congressional Hispanic Caucus. The New York senator said that if the Senate passes a bill by late spring or early summer, that would give the House "ample time" to pass a bill by the end of the year.
Reid said that he would use all his political will to get a bill passed.
"I'm committed to getting this bipartisan issue that we now have before us over the finish line,"he said.