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 has 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.