SAYNER, Wis. » After Gov. Scott Walker, a Republican in his first months in office, announced early this year that he wanted to cut collective bargaining rights for public workers, relations between political parties in his newly red state Capitol fell into a long, deep frost.

But after six months of bruising partisan fights, Walker seemed to issue an utterly different message this month. He said he wanted to meet with Democrats and to find shared agenda items — an invitation that has been met with polite acceptance and deep skepticism.

"My thought is, you start out with small things, you build trust, you move forward, you keep working on things and you try and pick as many things that are things that people can clearly work together on," Walker, who may face a recall election next year, said in an interview.

In the months after a flurry of Republican wins of governors’ offices and state legislatures in 2010, perhaps nowhere was the partisan rancor more pronounced than in the nation’s middle — places like Wisconsin and Ohio, where fights over labor unions exploded. But now, at least in those states, there are signs that the same Republicans see a need to show, at least publicly, a desire to play well with others.

In both states, critics dismiss the moves as desperate attempts to shore up sinking popularity ratings or disingenuous, tardy strategies to appear agreeable after already ramming through their agendas.

"It’s all PR — none of it is substantive," Mark Miller, the Democrats’ minority leader in the Wisconsin state Senate, said earlier this month, before Walker held what some described as a "cordial" meeting with the Democratic leaders last week.

Whatever the true substance of the offers, the recent tones in Ohio and Wisconsin do appear to show one thing: With threats of recalls and bill repeals, with public dismay in recent months over the partisan stalemate in Washington on the debt ceiling, and with battleground-state presidential politics looming in 2012, governing with majorities has turned out in some states to be more complicated than it may have first appeared.

Across the nation, partisan relations in statehouses where Republicans made significant gains last fall have varied widely, and in many cases there are no signs of softening messages — or even the need for such a thing. But leaders in other states, including some that are expected to consider limits to unions in the months ahead, are closely watching what unfolds now in Ohio and Wisconsin, the states that became the unexpected battle zones for an earlier season of discontent.

In Columbus, Democrats and union leaders were enraged this year when John R. Kasich, another first-term Republican governor, and the Republicans who now control both chambers of the legislature pushed through — mostly along partisan lines— a law that would limit the rights of public workers to bargain collectively.

Republicans in Ohio advocated for the measure as the logical response to shrunken budgets in towns, cities and counties. But union leaders and Democrats — and a group calling itself We Are Ohio — spent months collecting more than 900,000 valid signatures (hundreds of thousands more than needed) to put the law to a vote in a statewide referendum in November. A campaign, which is expected to draw significant interest and spending from political groups in Ohio and nationwide, is likely to begin in earnest soon.

Last week, Kasich and Republican leaders sent a letter to the union organizers, calling for a meeting to discuss a compromise. The leaders said they still believed in the law they had passed, and a spokesman for Kasich would not say precisely what areas the Republicans were willing to give in on. "We are prepared to move forward immediately with legislative action to implement any agreement on changes we are able to reach together," the letter read.

But critics balked at the notion that any real talks had been offered before or that any true, concrete compromises — not just photo opportunities for a public fatigued by partisan rancor — were being offered now.

"If they’re honestly coming forward for a compromise, repeal the bill and then we’ll talk," said Melissa Fazekas, a spokeswoman for We Are Ohio, explaining why representatives for the group had declined to meet with Kasich on Friday. "If they wanted to get along, they probably should have tried to during the legislative process instead of locking people out."

In Wisconsin, partisan relations — and that state’s fight over limits to collective bargaining — have proved still uglier.

In the weeks after Walker proposed the limits in February, state lawmakers, newly dominated by Republicans in the Capitol, split in two. The minority Senate Democrats fled the state to try to block a vote on the measure. The Republicans issued the lawmaking equivalent of warrants against them, and at one point, threatened that the Democrats had to collect their paychecks in person — or not get them at all. And, as protesters screamed outside his closed office door, Walker firmly defended the bargaining cuts and said his administration was "certainly looking at all legal options" against the other party.

But after a summer of expensive, brutal recall election efforts against nine state senators — Democrats for having fled the state, and Republicans for having supported the bargaining cuts — Walker seemed to be sounding a different, softer note. He said he had called Democratic leaders in the Legislature even before the polls closed in some of this month’s recalls, which, in the end, maintained the Republican majorities in both legislative chambers, though by a slimmer margin of 17 to 16 in the Senate.

Reflecting on the start of his term, Walker said that he wished he had spent more time "building a case" with the public for why for collective bargaining cuts could shore up budgets, but that he remained a firm supporter of the cuts themselves — a fact that seems certain to complicate any effort for bipartisanship now.

"I’m not thinking that just because we snap our fingers that suddenly everybody’s going to run out and work together and it’s all going to work perfectly," the governor said.

© 2011 The New York Times Company