Democrats are struggling to respond to a major redistricting setback in Virginia, with some party leaders discussing an audacious and possibly far-fetched idea for trying to restore a congressional map voided by the court but showing little indication they have a clear plan.

During a private discussion on Saturday that included Democratic House members from Virginia and Representative Hakeem Jeffries of New York, the minority leader, the lawmakers vented anger at their defeat at the Virginia Supreme Court, spoke about a collective determination to flip two or three Republican-held seats under the existing map and discussed a bank-shot proposal to redraw the congressional lines anyway, according to three people who participated in the call and two others who were briefed on it.

They did not land on a specific course forward, and Mr. Jeffries and the other members of Congress agreed to consult with their lawyers about the most prudent way to proceed, said the people, who spoke on the condition of anonymity to describe a private talk.

The conversation reflected the desperation and fury that have gripped the party after the state Supreme Court struck down a favorable map that had been ratified by voters. The most dramatic idea they discussed — which would involve an unusual gambit to replace the entire state Supreme Court, with a goal of reinstating their gerrymandered map — drew mixed reactions on the call, said the people, and it was not clear that it would even be viable, or palatable to Gov. Abigail Spanberger and Democrats in the Virginia General Assembly.

After Democrats had fought Republicans to a rough draw last month in a nationwide gerrymandering war, a pair of recent court rulings quickly gave the G.O.P. the clear upper hand in the race to redraw maps ahead of the midterm elections. Facing stiff headwinds, including President Trump’s low approval ratings and high gas prices, Republicans are looking for every advantage they can find to defy the odds and hold on to their narrow majority.

Any plans to enact a new congressional map for this year’s midterm elections would require action in the next few days. In a court filing last month, Steven Koski, the commissioner of the Virginia Department of Elections, said any changes to the maps after Tuesday, May 12, “will significantly increase the risk” of his agency being unable to properly prepare for the state’s scheduled Aug. 4 primary election.

A spokesman for Mr. Jeffries declined to comment.

Scott Surovell, the majority leader of the Virginia Senate, declined to comment on Saturday evening. Don Scott, the speaker of the state House of Delegates, said in an interview that he had not spoken to Mr. Jeffries or members of the congressional delegation about the multistep proposal that came up in the discussion.

One key to the plan would be having Democrats in Richmond lower the mandatory retirement age for state Supreme Court justices, an idea that began circulating among state lawmakers and members of Congress after a column proposing a version of the idea was published on Friday night in The Downballot, a progressive newsletter.

Ms. Spanberger would have to sign off on any legislation that lowered the judicial retirement age. She has not been briefed on the proposal, the people involved in the discussion or briefed on it said. Her spokeswoman, Libby Wiet, declined to comment.

The first step in the process, as discussed on the delegation’s call, would be to invoke a January ruling by a circuit court judge in Tazewell County, Va., that said the 2026 constitutional amendment effort to redraw the maps was invalid because county officials did not post notice of it at courthouses and other public locations three months before a general election.

Democrats would aim to use that ruling to seek to invalidate the earlier constitutional amendment that created the state’s independent redistricting commission by arguing that courthouses across the state did not post notice of it at the time. That would give the legislature the authority to enact a map of its choosing.

Ensuring the plan proceeds would involve the General Assembly, which is controlled by Democrats, lowering the mandatory retirement age for Virginia’s Supreme Court from 75 to 54, the age of the youngest current justice, or less. Virginia judges are appointed by the General Assembly, where Democrats hold majorities in both chambers and could then fill vacancies on the court with sympathetic Democratic lawyers.

Mandatory retirement ages are in place for judges in 32 states and Washington, D.C., according to a 2015 law review article from the Duke University Law School. The article said the most common retirement age set by states is 70.

In states such as Arizona, Georgia and Utah, Republican lawmakers have expanded state Supreme Courts in order to make them more conservative. But the Virginia proposal, which would get rid of all the sitting judges, would go considerably further.

Former Representative James P. Moran, Democrat of Virginia, said a move to stack the Virginia Supreme Court would be “just a bridge too far” and could backfire on his party.

He said he understood that many Democrats felt that their party “needs to fight back and not just be victims of unparalleled aggression.” But, he added: “We do have to keep our credibility. We have to do things that pass the legitimacy test.”

Representative Suhas Subramanyam, a Democrat who represents Loudoun County, Va., said in an interview that he supported doing whatever was necessary to preserve the map voters approved in last month’s referendum — including replacing the state’s Supreme Court justices.

“Everyone has got to have a strong stomach right now; this is a complete disaster waiting to happen if people are timid,” said Mr. Subramanyam, who was on the Saturday call. “We have Republican states ignoring their constitutions and interrupting early voting and ignoring their Supreme Courts all together. We know based on that, Republicans would explore every single option possible to move this forward.”

On Friday, Democratic legislative leaders in Virginia signaled that they planned to appeal the state Supreme Court ruling to the U.S. Supreme Court. But some legal experts believe the state court ruling could be the final word on the matter, because it does not involve federal law or the U.S. Constitution.

Mr. Jeffries has maintained throughout the redistricting battles over the last year that he would maintain all options for creating or preserving Democratic House districts and has said repeatedly that Democrats would employ “maximum warfare, everywhere, all the time.”

In an interview on Friday night, before his Saturday meeting with Virginia lawmakers, Mr. Jeffries said he was “exploring how to unravel this decision.”

“It’s an all-hands-on-deck moment, and it’s unprecedented in American history as far as we can tell that an actual election has been overturned by a handful of unelected judges,” Mr. Jeffries said. “We’re not going to step back, we will continue to fight back.”

Tim Balk contributed reporting.