The Senate Judiciary Committee approved, 12-10, Sen. Lindsey Graham’s asylum overhaul bill that aims to stanch the flow of migrants to the southwest border.

But the vote came amid loud protests from Democrats that the legislation was hastily pushed through. Democrats said Graham, the committee chairman, broke from longstanding committee procedures in scheduling a markup for Thursday and not allowing any Democratic amendments.

The legislation, which has little chance of passing in the House, was approved with one manager’s amendment. It now heads to the Senate floor, where Graham said he wants the measure to become part of larger negotiations between the House and Senate over the Homeland Security appropriations bill after the recess.

“I don’t want a stand-alone vote unless we have to, because I want to make it part of a bigger project,” Graham said after the vote. “And that bigger project is during the appropriations process.”

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Graham said that other immigration policy changes could be part of that discussion.

“I think the only way you actually get this thing fixed is a broader deal,” he said. “More money for border security, TPS relief, you know, people losing their status. They’re trying to say Venezuelans have to go back. There’s moving parts here that this bill can be part of.”

Graham said a “mini deal” on immigration was possible but it would have to include some changes to asylum law. He said he has been talking with House Speaker Nancy Pelosi and he thought some compromises are possible.

But Senate Minority Leader Charles E. Schumer rejected Graham’s suggestion about adding the measure to the appropriations debate, saying he “can’t imagine” the House accepting any appropriations measure that includes Graham’s asylum bill. Schumer said piecemeal approaches to immigration don’t work and Congress and the president should work on a comprehensive overhaul using the bipartisan 2013 Senate bill as a base. “Let’s go back to it. That’s the answer,” he said, referring to the so-called Gang of Eight proposal that Graham co-authored.

At the outset of the markup, Graham said the intent of the bill was to reduce the flow of migrants to the border. “We need to cut this flow off,” he said.

The bill, in broad strokes, would strip several protections for migrant children and generally make it much more difficult to obtain asylum in the United States. It also would give more power to the Department of Homeland Security to make decisions on migrants without going through judicial review.

In particular, the legislation seeks to modify the Flores agreement — a 1997 court settlement that requires migrant children to be placed in the least restrictive setting, and released from custody “expeditiously.” A recent court ruling interpreted the limit on detaining children to 20 days.

Graham’s bill would lift that limit and also loosen standards of care for children in government custody. Some provisions in the bill would also make it more difficult for abused and neglected children to receive protection in the United States. These measures, Graham has argued, would create disincentives for migrants from making the dangerous journey to the border.

Thursday’s markup was short and marked by drama: Democrats argued Graham rushed through approval of the bill by sidestepping committee procedure and without much debate or room for amendments from Democrats.

The panel approved a motion by Graham to go straight to voting on his manager’s amendment and then report the bill to the Senate floor.

Afterward, ranking member Dianne Feinstein of California lamented that the bill did not “enjoy broad support” and that “it would increase problems at the border.” She said that a number of Democrats had requested that the bill be held over until after the August recess, and that Graham’s refusal to do so was a violation of procedure.

“No matter how many committee rules or Senate rules are broken, this bill will not become law,” she said. “It begs the question: Why are we doing this?”

Sen. Patrick J. Leahy, who has enjoyed a decadeslong tenure on the committee, said that it “is not what it used to be.” In a dramatic gesture, he tore up a copy of the committee rules, which he noted every member had voted on six months ago. The Vermont Democrat called the committee “a conveyor belt of ultra partisan ideas.”

“This is supposed to be the Senate Judiciary Committee — not the Donald Trump committee,” Leahy said.

Graham defended himself by saying the markup on the bill was scheduled last week but only one Democrat was present. Without at least two members of the minority, the committee did not have a quorum and could not take action on the bill that day.

“I’m responding to what you did last week — last week you chose not to show up … what am I supposed to do?” Graham said in response to Feinstein’s opening. “I would expect you to do what I’m doing if this happens in the future” and the tables were turned, he added.

Before the markup, about 150 immigrants’ rights organization signed onto a letter opposing the legislation, arguing that it would “foreclose lifesaving protection and subject children as young as toddlers to prolonged and harmful incarceration.”

In a statement, the advocacy organization America’s Voice argued that Graham’s position had shifted greatly since 2013, when he was one of the main players working on a comprehensive, immigration overhaul as part of the Gang of Eight of bipartisan senators.

“As Senator Graham performs today for an audience of one, those of us who knew him when mourn the loss of a leader who once fought bravely for great causes and now fights cravenly for a cruel man,” the organization said in a statement.

After the bill was approved, several Democrats raised points of order, objecting to the way the markup was conducted. “I am sick at heart at what we’ve done — I hate being here right now, I hate what has just happened here,” said Sen. Sheldon Whitehouse of Rhode Island. “If the chairman’s reading of rule 26 is given any credence, then we are in the majority free-for-all, where no rule, no procedure, no principle, no protocol, and no courtesy matters any longer.”

Sen. Mazie K. Hirono of Hawaii ended the session by remarking on the substance of the bill, given that no amendments from Democrats had been allowed. “This gives so much power to administrative decision making that in a word, it’s nuts — and probably unconstitutional.”