Sen. Charles E. Schumer said Sunday that a bipartisan group of eight senators is “on track” to introduce comprehensive immigration legislation by the end of this week, despite recent “kerfuffles” in its negotiations and competing items on the congressional agenda.

“I think we’re doing very well,” the New York Democrat said on CBS’ “Face the Nation.” “We hope that we can have a bipartisan agreement among the eight of us on comprehensive immigration reform by the end of this week.”

The Senate group’s timetable has been called unrealistic by some advocates, given that the week is shaping up to be packed for lawmakers.

On Tuesday, senators will return from their two-week spring recess and take up the most comprehensive set of gun control legislation in nearly two decades. Schumer and other senators are still trying to reach consensus on one contentious aspect of that legislation — universal background checks on gun sales — and will be under intense pressure to reach a deal that is amenable to members of both parties.

On Wednesday, President Barack Obama will introduce his fiscal 2014 budget blueprint, which is certain to distract from both the gun debate and the status of the draft immigration legislation.

Schumer said Sunday that lawmakers’ staff have been hard at work in ironing out final legislative language. He said complications in the negotiations have been “kerfuffles” and not major stumbling blocks.

“I don’t think there’s any main sticking point,” he said.

Schumer and Sen. John McCain, R-Ariz., also rejected concerns from Republicans on the Senate Judiciary Committee that the immigration bill is being secretly negotiated and would be rushed through the legislative process.

Schumer said that the bill would go through a Judiciary markup — likely by “some point in May” — and that opponents of the legislation “will be able to shoot at it in committee.”

McCain, appearing alongside Schumer on “Face the Nation,” agreed.

“I reject this notion that something is being railroaded through,” he said. “This is the beginning of the process, not the end of the process.”

Elsewhere, two members of a bipartisan House group that is negotiating its own immigration proposal — Mario Diaz-Balart, R-Fla, and Luis V. Gutierrez, D-Ill. — declined to say Sunday when their bill would be introduced.

“Our concern is to get it done well, not quickly,” Diaz-Balart said on CNN’s “State of the Union.”

Diaz-Balart said the two chambers’ bills are likely to be very different, given that the Senate is led by Democrats who insist on a pathway to citizenship for those here illegally and that the House is led by Republicans who have expressed concern about such a plan.

Conference negotiations between the House and Senate “could be difficult,” he said. “But so far it looks like we’re at least on the same planet.”

Sen. Lindsey Graham said on NBC’s “Meet the Press” on Sunday that final legislation would need to balance the GOP’s emphasis on border security with Democrats’ insistence on a pathway to citizenship.

“We are going to secure that border and it will be tied to a pathway to citizenship or there will be no deal,” the South Carolina Republican said, adding that he is 70 percent confident that lawmakers will be able to reach agreement after years of failed attempts.