In Minnesota, Democratic legislators are threatening to stay away from the state capitol this week to prevent Republicans from trying to claim control of the House of Representatives.

In Michigan, Republican senators, who are just one seat behind the Democrats, want a special election as soon as possible to fill a seat they believe can be flipped.

And in Virginia, Democratic candidates in three special elections last week were pushing hard to retain their majorities in both legislative chambers, as Democrats try to enshrine abortion rights in the state’s constitution.

As state legislatures convene around the country this month, several knife-edge fights for partisan control have magnified the degree to which political polarization has become ingrained, not just in Congress, but in statehouses across the country.

The battle to gain the upper hand puts pressure in particular on Democratic lawmakers, who, unlike the past four years, face even higher stakes. They are already are playing defense as President-elect Donald J. Trump prepares to take office again, bolstered by the Republican takeover of Congress.

“With Trump and his MAGA allies in the states returning to office, building and defending Democratic power in the states is essential,” said Heather Williams, the president of the Democratic Legislative Campaign Committee.

Republicans now control a majority of statehouses. But Democrats captured four state legislatures in 2022, and they parlayed that power into progressive laws related to abortion, voting rights and more.

In 2024, though, Republicans, arguing that Democrats had gone too far, regained the majority in the Michigan House, tied in the Minnesota House and made strong inroads in Vermont.

Since Election Day, the most dramatic battle has been unfolding in Minnesota. State Senator Kari Dziedzic, a Democrat from Minneapolis, died of cancer, leaving the chamber deadlocked at 33-33.

“There’s nothing that can be done until a special election happens,” Representative Lisa Demuth, the House Republican leader and speaker-designate, said in an interview. “The problem with saying, ‘Well, it’ll be in a couple of weeks, we should just act like we’re at 67 anyway’ — that’s not how math works.”

She has also suggested that a Republican majority would refuse to seat Representative Brad Tabke, a Democrat who won re-election by 14 votes after 20 absentee ballots were lost. Six of those 20 voters later testified that they had voted for Mr. Tabke, giving him an insurmountable margin. A judge is expected to rule at any moment, but Ms. Demuth said there should be a special election, regardless of what the judge decided.

In response, Democrats have floated the possibility of boycotting the session, with the aim of denying the Republicans the necessary quorum — a majority of total members must be present — to kick it off.

Recent walkouts elsewhere have underscored the partisan divide. In Texas, House Democrats fled the state for Washington in 2021 to temporarily deny Republicans the two-thirds quorum needed to pass a restrictive voting measure.

In Oregon — which also has a two-thirds quorum requirement — Republican Senators intent on stalling bills on climate policy, taxes and abortion walked out so frequently that voters altered the state constitution to ban such absenteeism. Most Republican Senators were also barred from seeking re-election.

But a walkout of the kind being discussed in Minnesota would be without precedent, said Bill Kramer, the vice president and counsel of MultiState, a state and local government relations firm.

“I can’t remember any time where it’s been like this at the very start of session,” he said. “You put the rules in place, you elect a speaker, you elect committee chairs — all of those types of things which put in place the agenda procedurally for the next two years.”

In Virginia, two of the contests last week were for the Senate, and one for the House; before these special elections, Democrats were clinging to single-vote majorities in both chambers, which they claimed when they won the House in 2023. At stake, to some degree, was the agenda of outgoing Republican governor Glenn Youngkin, who is prevented by the state constitution from running for a second term.

Turnout was light for the election in Loudoun County, where one House race and one Senate race were on the ballot. Harish Sundaraman, 24, said he was voting for both Democrats, even though he did not fully subscribe to the party’s policies. He would have liked to have known a little more about the candidates, he said. But he was motivated by his views on abortion rights, which Democrats hope to advance in the coming legislative session.

“I thought if I vote Democrat in this local election, it might be helpful,” said Mr. Sundaraman, who works in information technology in Washington, D.C.

Ultimately, two Democrats and a Republican prevailed, leaving the balance of power unchanged.

Overall, Republicans now control the legislature in 28 states, and Democrats 18. (The other states are split, unresolved or led by a bipartisan coalition.)

A single vote can be momentous, even in states where one party dominates. In North Carolina, a legislator who unexpectedly switched her party affiliation from Democrat to Republican enabled Republican leaders to enact a 12-week limit on most abortions in 2023, overriding Gov. Roy Cooper, a Democrat.

Few sitting state legislators have had more experience with the whiplash of paper-thin margins than the members of the Pennsylvania House. After 2022, Pennsylvania was one of only two states where different parties held control of the legislature’s two chambers. Though Republicans held a comfortable majority in the Senate, the Democrats’ hold on the House was nerve-wrackingly precarious, at times vanishing altogether.

In 2024, despite losses by Democrats in the presidential race, a U.S. Senate seat and several Congressional seats, not a single seat in the Pennsylvania House of Representatives flipped. The Democrats thus maintained the same one-seat majority they had two years earlier.

Then, in December, a Democratic member had a medical emergency, and he has been in the hospital ever since. As it had multiple times in the previous two years, the House returned to a functional tie.

But when House members gathered on Tuesday, the first day of the new session, the election of a speaker went forward smoothly and relatively quickly, without the backroom deals and prolonged drama that had surrounded the vote two years ago. Partly as a result of compromises with Republicans over House procedural rules, the legislature promptly re-elected the previous Democratic speaker in a voice vote.

“I think everybody has learned their lesson,” said Representative Michael Schlossberg, a Democrat, describing himself as the “majority whip with no room for error.” The last two years have had their challenges, he said, but a narrow partisan margin does have its advantages, forcing compromise and discipline.

As for lessons for his counterparts in other states, he offered this: “Do not confuse short-term advantage with long-term advantage.”

And, mentioning various maneuvers for partisan gain that had ultimately backfired, he added: “Don’t get too cute.”

Courtney Mabeus-Brown contributed reporting from Loudoun County, Va.