Senator Chuck Schumer of New York, the minority leader, is facing a torrent of criticism for choosing to vote with his Republican counterparts to head off a government shutdown.

Some of the sharpest barbs have come from another New York Democrat, Representative Alexandria Ocasio-Cortez.

Ms. Ocasio-Cortez blasted Mr. Schumer’s efforts to gather enough Democratic support so Republicans can clear a procedural hurdle and pass a measure to fund the government through Sept. 30, accusing him of ceding the sliver of power Democrats had over President Trump.

“I believe that’s a tremendous mistake,” she said in a CNN interview on Thursday.

And she had specific criticism of the legislation itself. “This turns the federal government into a slush fund for Donald Trump and Elon Musk,” she said. “It sacrifices congressional authority, and it is deeply partisan.”

Her sharp remarks even stirred talk about whether she would consider challenging Mr. Schumer, 74, in a primary when he is up for re-election in 2028. Asked directly in the television interview if she would consider such a campaign, she sidestepped the question but did not shoot down the premise.

The House Democratic leadership — with yet another New York legislator at the top — quickly followed Ms. Ocasio-Cortez’s criticism, putting out a statement knocking Mr. Schumer’s caucus for going along with Republicans. All but one House Democrat voted Tuesday against the plan, which would slightly decrease spending overall.

“The far-right Republican funding bill will unleash havoc on everyday Americans, giving Donald Trump and Elon Musk even more power to continue dismantling the federal government,” Representative Hakeem Jeffries of New York, the top House Democrat, said in a joint statement with the rest of his leadership team.

“House Democrats will not be complicit,” they said.

Their anger, with Ms. Ocasio-Cortez out front, reflects a boiling over of resentments among some Democrats about the gerontocracy leading their party. The older generation led them astray last year during the presidential election, many younger Democrats say, and it is hurting them again as they try to stand up to Mr. Trump.

Angered House Democrats were already discussing primary challenges to Mr. Schumer, who was first elected in 1998.

“Schumer has been in politics for a long time, and I would hope that this is his final term, and he opens it up for someone new,” said State Senator Jabari Brisport of New York, an ideological ally of Ms. Ocasio-Cortez, who endorsed him when he first ran.

Mr. Brisport said that he did not know if Ms. Ocasio-Cortez aspired to higher office. But if she ran, he said, “she would make a fantastic senator.”

Mr. Schumer’s defenders note that it was easier for House Democrats to vote no — because the Republicans in their chamber had enough support to pass the legislation to keep the government open without Democratic help.

And, his defenders say, allowing the government to shut down would only make matters worse.

It “may feel good giving vent to our frustration,” Jay Jacobs, the New York Democratic Party chair, said in a statement. But it “will work against our long-term desire to win back the Congress in 2026 and the presidency in 2028.”

In television interviews, floor speeches and a New York Times opinion piece, Mr. Schumer defended his choice, saying that he hated the bill before him but that its passage was better than a shutdown.

“The risk of allowing the president to take even more power via a government shutdown is a much worse path,” Mr. Schumer wrote in The Times.

His efforts drew praise from perhaps an unwelcome source: the president himself.

“Congratulations to Chuck Schumer for doing the right thing — Took ‘guts’ and courage!” Mr. Trump said on social media.