The States Project, a deep-pocketed outside group focused exclusively on state legislatures, is adding the Wisconsin State Assembly to its 2024 plans, a clear sign that Democrats are growing bullish on an opportunity to flip the chamber after the State Supreme Court ordered new maps to be drawn this year.

The organization said that it would include Wisconsin in its eight-figure 2024 budget and spend an additional $1 million there. (The group has not yet completed its 2024 total spending plans.) State legislative races, which play out in smaller districts than contests for Congress do, are often much less expensive than federal races. Large donations in these elections can have a significant impact.

National Democrats have zeroed in on the Wisconsin Legislature. The Democratic Legislative Campaign Committee, the state legislative arm of the Democratic National Committee, has already donated $24,000 directly to each chamber of the Legislature, the maximum legally allowed, and it has added Wisconsin to its national $60 million budget. Forward Majority, another outside group focused on state legislatures, plans to spend heavily in the state after spending more than $1 million in 2018.

The deluge of cash and attention into the Wisconsin Legislature presages a possible shift in the state’s politics. Dominated by extreme partisan gerrymanders for more than 13 years, both chambers of the Legislature have remained solidly in Republican control, even as Democrats have won statewide races for governor, Senate and the presidency in multiple elections.

The Republican State Leadership Committee, the arm of the Republican National Committee that focuses on state legislative races and others down the ballot, has not yet released a budget but did include Wisconsin on its initial list of states where it plans to defend majorities. A spokesman for the organization did not respond to requests for comment.

The new maps will make Wisconsin even more of a battleground, with President Biden and former President Donald J. Trump neck and neck in recent polling. But even with the new maps, Democrats acknowledge that flipping the chamber will be an uphill battle.

“Maps can make a chamber uncompetitive, but maps aren’t going to win a chamber,” said Daniel Squadron, a former Democratic state senator from New York and co-founder of the States Project. He pointed to the recent Democratic successes in flipping chambers in Michigan and Pennsylvania after significant redrawing of maps after Republican gerrymanders.

“Good candidates who have a great relationship with their constituents or their voters, who have a good recognition of who their voters are,” were the most successful in Michigan, Mr. Squadron said.

Democrats are hoping to find similar success in Wisconsin, including at the top of the 2024 ticket. And some organizations see the political realignment brought by Wisconsin’s new maps as a potential boon for the Biden campaign.

“These candidates in these races give voters another reason to turn out when they may not be that excited about Biden, given his abysmal approval rating,” said Vicky Hausman, a founder of Forward Majority, a Democratic super PAC. “There’s a lot of vibrance down ballot, with state legislatures being part of the story of 2022 and hopefully the story of 2024.”

The States Project is also expanding into North Carolina, joining an effort by other Democratic groups, including the Democratic Legislative Campaign Committee, to break up the state’s Republican supermajority in the legislature. The focus on the state legislative races will only compound the political pressures in North Carolina, which will host the most closely watched governor’s race in 2024 and which is emerging as a key target for Mr. Biden’s re-election campaign.