Eight US senators crafting an overhaul of immigration policy are on the verge of finalizing a deal that could bring 11 million undocumented migrants out of the shadows, one of the lawmakers said Thursday.

Senator Chuck Schumer, the leading Democrat in the bipartisan Gang of Eight, said the plan, which members of the group said will include a "pathway to citizenship," was on track for completion by the end of the month.

"We are very close to agreement," Schumer told reporters after the senators met for two hours in their ongoing effort to forge the biggest reform to immigration laws since 1986.

"We're meeting again this afternoon. And we expect to meet our goal of having comprehensive immigration reform... supported by all eight of us."

Schumer was speaking after protesters supporting immigration reform entered his office in the Hart Senate Office Building demanding a timely unveiling of the senators' plan.

"I understand people's frustration. People have waited a long time," Schumer said. "But we are real close for the first time to coming up with a bipartisan agreement that has a darn good chance at becoming law, and we'll need all the support we can get."

The sensitive and highly complex issue has gained currency since last November when Democratic President Barack Obama won re-election with overwhelming Hispanic support.

Earlier this week the Republican National Committee issued an election "autopsy" and stressed that the party must "champion comprehensive immigration reform" as part of its effort to attract Hispanic voters.

The White House is putting together its own backup plan in the event the senators fail to produce, and some of the provisions are said to be similar.

The Gang of Eight, including Republican Marco Rubio, a possible 2016 presidential prospect, announced in January that their plan would aim to offer a pathway to eventual citizenship, taking up to 13 years or more, for millions of illegal immigrants already in the United States.

Such a move would be contingent on pre-conditions including steps taken to better secure US borders and institute an employee verification program.

But sticking points have stalled the plan's final roll-out, notably the issue of the "future flow" of immigrants into the United States and the number of guest worker visas that Washington will provide, particularly to highly skilled people in technical, scientific or medical fields.

Should the bill pass the Senate, its steepest hurdle may be in the Republican-led House of Representatives. House Speaker John Boehner says he backs comprehensive reform, but it could prove difficult to bring conservative members on board.

A new poll by the Public Religion Research Institute and the Brookings Institution shows 63 percent of Americans, including 53 percent of Republicans, favor a path to citizenship -- with conditions -- for the millions of undocumented immigrants.

Just 21 percent of respondents thought the illegals should be found and deported.

Despite the optimism, Senate Judiciary Committee chairman Patrick Leahy has denounced the delays by the lawmakers huddling in "secret" over their plan.

Leahy wanted time for members and the public to review the proposal over a two-week congressional recess.

But without legislative language to debate, the committee "will not be able to report a comprehensive immigration bill by the end of April, which was my goal," he said.