Late on Nov. 8, 2016, the mood inside President Barack Obama’s West Wing turned grim. Hillary Clinton was coming up short. The realization was growing that Donald J. Trump would be elected president.

Suddenly, David M. Simas, Mr. Obama’s political director, pumped his fist and called out, “Yes!”

A cautious, cerebral lawyer, Mr. Simas was not known for attention-getting exultation. Asked why he was cheering, he deadpanned: “We just won a North Carolina Supreme Court seat.”

Incongruous as it was, the moment of triumph in a relatively minor contest reflected a growing concern among Democratic leaders, all the way up to Mr. Obama, that their party needed a more assertive strategy for the end-of-decade redistricting fights to come. But as Democrats awakened to the depth of their plight, they found that learning to think small was easier said than done: Hopes of big gains at the state level in 2020, a crucial year for redistricting, did not materialize. Liberal voters showed they were less hungry to win those races than they were to oust Mr. Trump.

Now, however, state-level contests like those for governor’s offices, legislatures and courts are suddenly moving from the periphery to the center of American politics. And the ongoing tussle over political maps is just one front in a larger conflict: As Mr. Trump pushes his false claims of a stolen 2020 election, what was once seen at most as a decennial scrum for partisan advantage in the provinces of government is transforming, in some Democrats’ minds, into a twilight struggle for the future of American democracy.

“We’re at a moment of reckoning in America,” former Attorney General Eric H. Holder Jr. said during a recent fund-raising event for the National Democratic Redistricting Committee, a group he formed that became the primary locus of Mr. Obama’s political activity when he left the White House. “I’m not being hyperbolic or alarmist. I think our democracy is on the line.”

Fund-raising appeals on behalf of Democratic legislative candidates note the fact that at least six Republican state lawmakers were in Washington on Jan. 6, and that Republican-led states from Arizona to Georgia have passed laws tightening the rules around voting. And revelations about Mr. Trump’s ad hoc efforts to overturn the previous presidential election are fueling fears that in a rematch of 2020, Mr. Trump might conspire with G.O.P. state lawmakers to alter the outcome illegitimately.

“We believe the right wing is signaling a strategy to steal the election through state legislatures in 2024,” said Daniel Squadron, a former New York state senator whose group, the States Project, has announced plans to raise $30 million to support Democratic candidates in state legislative races in 2022.

Yet it remains to be seen whether such dire warnings will move voters. Selling rank-and-file Democrats on the importance of offices like state senator or state Supreme Court justice has proved daunting. In the 2020 campaign cycle, donors showered Amy McGrath, a doomed Democratic candidate for Senate from Kentucky, with $96 million, dwarfing the $51 million raised by the national Democratic Party committee responsible for aiding candidates for legislative seats in all 50 states. And Democrats tend to suffer disproportionately from “roll-off,” a phenomenon in which voters fail to complete their ballots, withholding their votes from candidates at the bottom of the ticket.

“It feels very much like climbing uphill, pushing a rock while your arms are melting,” said Amanda Litman of the liberal group Run for Something, which recruits young people to run for state and local office.

Gaby Goldstein, co-founder of Sister District, a grass-roots organization that supports progressive candidates in state legislative races, noted that conservatives have mobilized around state politics for decades. “I always say that Democrats are tardy to the party,” she said.

The Democratic Party’s belated interest in lower-tier races grew out of its bruising experience in 2010, when Republicans rode an anti-Obama backlash to oust hundreds of Democratic incumbents nationwide. Spending just $30 million, Republicans flipped 680 state legislative seats and 20 chambers, a stunning victory that put them in position to redraw election maps and entrench their hold over those states — and their congressional delegations — for a decade.

“Democrats were frankly unprepared during that cycle,” said Kelly Ward Burton, who at the time was running House Democrats’ campaign committee. Now the president of Mr. Holder’s redistricting committee, Ms. Burton has been working closely with several Democratic campaign groups in hopes of a different outcome from the current round of redistricting.

Part hardball politics and part good-government activism, the groups’ strategy has been to break up G.O.P. “trifectas” where possible — reducing the number of states where Republicans enjoy full control of the redistricting process because they hold the governorship and majorities in both legislative chambers. They also ask candidates for state and federal offices to pledge support for “fair redistricting that ends map manipulation and creates truly representative districts,” an aspiration that is sometimes in tension with more partisan goals.

Midway through the current redistricting brawl, the results of those Democratic efforts are mixed.

The long-troubled Democratic Legislative Campaign Committee became a force under new leadership in 2016, setting up the party to take six chambers in the 2018 midterm elections. Since 2017, Democrats have flipped 10 governor’s offices, including in the battlegrounds of Michigan, Nevada, Pennsylvania and Wisconsin, and picked up seven state Supreme Court seats. Five states have passed nonpartisan redistricting reforms, putting map-drawing in the hands of independent commissions.

But the blue wave that Democrats were counting on in 2020 never washed ashore. Although Democratic groups spent record amounts trying to win back G.O.P.-held statehouses, their party ended last year worse off, losing both chambers in New Hampshire. As a result, Republicans not only kept control of prizes like the Arizona, Michigan, Pennsylvania and Wisconsin legislatures, but they also have retained the power to draw maps for 187 congressional districts, while Democrats control the fate of just 75.

As a result, Democrats’ hopes of keeping the House may rest on legal challenges to maps that Republican-led states have already approved. And a 2019 Supreme Court ruling, which put partisan gerrymandering claims beyond the purview of federal courts, ensures that state courts will be the main arena for such lawsuits.

In 2019, Democrats lost a crucial state Supreme Court contest in Wisconsin by fewer than 6,000 votes, cementing the body’s conservative majority. But the election of liberal judges in North Carolina and Ohio has given Mr. Holder’s group, and other liberal outfits allied with it, at least a chance to win in court what Democrats lack the power to achieve in Republican-dominated legislatures.

Elsewhere, high-minded sentiments are yielding to the demands of brass-knuckle politics. Many Democrats cheered the aggressive gerrymandering in Illinois, where maps approved by Gov. J.B. Pritzker could net them at least one additional House seat, and they are urging a similar approach in New York, where a Democratic supermajority may seek to gerrymander its way to capturing as many four seats currently held by Republicans.

None of which is lost on Republicans. “Democrats pretend to be for ‘fair maps,’ but they use every advantage they get,” said Andrew Romeo, a spokesman for the Republican State Leadership Committee.

But Democratic gerrymandering could backfire, cautioned Adam Kincaid, head of the National Republican Redistricting Trust. In several states that Democrats control, he noted, they have drawn new districts with only a slight partisan tilt, which could make them vulnerable in the event of a Republican wave. “It seems like Democrats are spreading their voters out to cover more territory,” he said.

And as Democrats gear up for what most acknowledge will be a difficult midterm election in 2022, the missed opportunities of 2020 and earlier election cycles loom large in the rearview mirror.

“It was a really bad day at the statehouses when Republicans won those races,” said David Pepper, a former chair of the Ohio Democratic Party and the author of a new book on state legislatures. “Almost as if Trump had won.”

In 2022, Democrats are focused on flipping several of the state legislatures that remained tantalizingly out of reach after 2020 — chiefly Arizona, Michigan and Pennsylvania. In North Carolina and Wisconsin, they are simply trying to stave off Republican supermajorities. They also must defend narrow majorities in Colorado, Maine, Minnesota and Nevada, and could be dogged by economic worries and President Biden’s dismal approval ratings.

Jessica Post, president of the Democratic Legislative Campaign Committee, acknowledged the rocky terrain ahead, but said new maps in Arizona, Michigan and Pennsylvania could present opportunities.

“We’re very cleareyed about what may happen out in the electorate,” she said, but she insisted that, “If we run good races, we can win in tough territory.”

The explosion of gerrymandering after the Republicans’ 2010 romp, however, has meant that few seats are truly competitive. Charles Nuttycombe, an analyst of state legislative elections, has calculated that between 2018 and 2021, only 15 percent of statehouse contests were decided by 10 percentage points or less.

“The bigger story here is that the Democrats are kind of in a rut, and I don’t know how they’re going to overcome the structural disadvantages they face,” said Michael J. Behm, a lobbyist who tracks legislative elections.

Mr. Obama’s assistance alone may not provide much of a lift. He has participated in several fund-raising events and virtual town halls held by Mr. Holder’s group, and he endorsed 21 candidates for Virginia’s House of Delegates. Five of them lost their seats as Republicans narrowly captured control of the chamber last month.

Reviewing the results in Virginia, Ms. Goldstein, a progressive activist, urged her party to develop a message that would inspire voters to reach all the way down the ballot.

“We cannot just be against deplorable stuff,” she said. “We absolutely have to be sharing a vision of the world that is exciting to people.”