In Madison, a full battle was underway.

“It’s an attack on the entire citizenry of Wisconsin,” Russ Hahn, 53, a lawyer from Kenosha, Wis., said of the Republicans’ efforts to push through limits on the incoming governor and attorney general. Mr. Hahn, who said he considers himself an independent, had come to the Capitol — as did hundreds of others — to protest as lawmakers debated the fate of the package inside the chambers. Mr. Hahn carried a sign that read, “GOP Grinch Stealing Democracy.”

“What they’re doing today,” Mr. Hahn said, “is a travesty.”

Republicans, who have controlled state government in Wisconsin since 2011 after they flipped both legislative chambers and the governor’s office, defended their efforts as long-needed changes to rebalance power, which they said had become tilted in favor of the executive branch.

Robin Vos, the speaker of the Assembly, said Republicans owed it to their voters to protect policies enacted under Scott Walker, the Republican governor who was defeated in November, and to institute checks on the power of the incoming Democrat, Tony Evers.

“These are the right things to do,” Mr. Vos told reporters. “We are going to make sure the powers of each branch are as equal as they can be.”

Mr. Walker’s eight years in Wisconsin have been punctuated by partisan tumult as Mr. Walker and his Republican lawmaker allies pushed state policies to the right on matters like union power and taxes. This purple state, which voted for Barack Obama but also helped seal Donald J. Trump’s electoral win in 2016, has been rived by partisan fighting in recent years.

After Mr. Walker proposed sweeping cuts to benefits and collective bargaining rights for most public sector union employees a few weeks into his administration in 2011, thousands of protesters packed the Capitol for days, setting off months of recall elections. Some of the protesters at the Capitol this week said they had marched here before — in 2011 or in other skirmishes since.