Immigration rights advocates are turning their fire on one of their own champions, Sen. Charles E. Schumer, demanding he stop taking donations from lobbyists for private prisons, which earn money by holding illegal immigrants for the U.S. government.

Advocates delivered petitions to Mr. Schumer’s New York City office on Tuesday and began walking the streets in heavily Hispanic neighborhoods in the city to raise the heat on the third-term Democratic senator, underscoring how worried they are that he will undercut them as he tries to negotiate a final immigration deal with seven other senators.

“His priorities have been really misguided in terms of focusing on more enforcement,” said Cesar Vargas, executive political director of the DRM Action Coalition, which was helping organize Tuesday’s events. “We’re bringing that [information] not only to us rallying in front of his office, but now we’re litigating his record to voters in the public sphere.”

Mr. Schumer, chairman of the Senate Judiciary subcommittee on immigration, refugees and border security, is one of eight senators working to strike a deal on a broad overhaul of the country’s immigration system, including extending citizenship rights to most of the estimated 11 million illegal immigrants in the U.S.

On the negotiating group are four Republicans and four Democrats. Of those Democrats, immigrant rights groups are most worried about Mr. Schumer, partly because they have looked at his political donations and found contributions from a handful of lobbyists who work for private prisons.

Peter Cervantes-Gautschi, executive director of Enlace, a group of community organizers in Mexico and the U.S., said the deal taking shape in the “Gang of Eight” appears to be heavy on border enforcement. He said that means business for private prisons that hold illegal immigrants as they await deportation or, in some cases, criminal proceedings for illegally crossing into the U.S.

“The attempt to put together a deal is going to result in the increased massive incarceration of immigrants in private prisons,” Mr. Cervantes-Gautschi said. “It’s really not hard to connect these dots.”

Mr. Schumer’s office didn’t respond to requests for comment Tuesday.

The advocates’ concerns over Mr. Schumer have simmered for years. He voted for the 2006 Secure Fence Act and was one of the chief backers of a 2010 bill that boosted the U.S. Border Patrol by 1,500 agents and added new technology and infrastructure to the southwestern border.

But he also has tried several times to negotiate a broader legalization bill. Attempts included talks with Sen. Lindsey Graham, South Carolina Republican, in 2011.

One former Capitol Hill staffer who has followed the players for years said the protests against Mr. Schumer stand in contrast to the other three Democrats in the negotiations: Sens. Robert Menendez of New Jersey, Michael F. Bennet of Colorado and Richard J. Durbin of Illinois.

“He’s saying all the right things and doing all the right things, but in the end he’s seen as much more politically inclined to cut a deal on enforcement than Sens. Menendez, Bennet and Durbin. So the idea here is just to let him know they’re watching him, and No. 2, highlighting the soft underbelly of this issue,” the former staffer said.

Not all immigration advocates are targeting Mr. Schumer.

“Sen. Schumer’s role has been increased importance in framing the issues and getting the bipartisan progress going after the election,” said Chung-Wha Hong, executive director of the New York Immigration Coalition, a broad umbrella for dozens of groups.

She said her coalition is focused not so much on the people as much as on the bill they are writing, and she said they will be vocal in advocating for the parts of the deal they like and opposing those parts they don’t.”The bill will speak for itself,” she said.

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