A key member of a bipartisan Senate group said Thursday that the eight members are nearing agreement on a comprehensive plan to overhaul the nation’s immigration laws and will unveil a bill for consideration early next month.

The comments from Sen. Charles E. Schumer (N.Y.), the group’s leading Democrat, came in response to rising frustration over the pace of the talks. Two dozen advocates protested inside Schumer’s office Thursday, leading to the arrest of several members. The demonstration by CASA in Action illustrated the raw emotions of the debate even as momentum builds for a bipartisan agreement that would include a path to citizenship for the nation’s 11 million illegal immigrants.

Organizers of the protest said they were unhappy that the senators will not complete their work before leaving Washington on Friday for a two-week Easter break. The senators, whose bill is expected to be a template for a deal between Congress and the White House, had hoped to introduce the legislation this month but now have pledged to do so shortly after returning April 8.

Outside his office, Schumer sought to calm tensions by telling the protesters, “We’re on your side,” according to a spokesman.

“The group remains on pace to complete a deal by the end of the month,” Schumer said. “In fact, we are very, very close to a final agreement.”

In addition to potential citizenship for undocumented migrants, the comprehensive bill is expected to include a new program for foreign workers that would add up to 200,000 visas per year depending on economic conditions and employment needs. However, lawmakers continued to negotiate Thursday over the terms of how much those workers would be paid, people familiar with the negotiations said. The legislation also is likely to increase significantly the number of visas for highly skilled tech workers, reduce some categories of family visas and increase border control and workplace security measures.

The confrontation at Schumer’s office came in the wake of pronouncements by several high-profile Republicans, including Sen. Rand Paul of Kentucky and former Mississippi governor Haley Barbour, in support of immigration reform. A new Public Religion Research poll Thursday found that 63 percent of Americans support offering illegal immigrants a chance to earn citizenship provided they satisfy some requirements, with just 21 percent saying they should be deported.

But the advocates say they are concerned that the timetable is slipping as illegal immigrants continue to face arrest and deportation. “There are 11 million people, and the tens of millions more who know and love them, waiting for Congress to act,” CASA in Action organizing director Gustavo Andrade said in a statement. “Get it done now.”

On Wednesday, Sen. Patrick J. Leahy (D-Vt.), chairman of the Judiciary Committee, which will oversee the markup of an immigration bill, publicly complained that the bipartisan Senate group’s delay means his committee will not be able to approve legislation in April, as he hoped.

With the high stakes involved, the group has made a concerted effort to keep the substance of the talks confidential and to stem leaks about the evolving legislation. After one leak last week, Sen. John McCain (R-Ariz.) admonished the group, reminding members that they had promised to keep the talks quiet, said a Senate aide, who requested anonymity because he was not authorized to speak publicly.

“I’m not discussing what we’re discussing,” McCain told reporters Thursday. “It’s one of the things frankly that’s hurt, these selective leaks that have gone out.”

The White House has publicly supported the Senate group’s principles, and President Obama has tried to stay out of the spotlight since a late January speech in Las Vegas in order to give the senators time to work out a proposal. Administration officials have said the president will step in with his own legislation if the Senate group fails to produce a bill.

“We’re calling for the president and the House to take action now,” said Angelica Salas, executive director for the Coalition for Humane Immigrant Rights of Los Angeles.

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