But Democrats say such overtures are more smoke and mirrors rather than a desire for substantive discussions about the direction of their states, The New York Times reported.
Wisconsin Republican Gov. Scott Walker and legislative Democrats squared off in a bitter fight over Walker's plan to sharply curtail public union benefits and the collective bargaining process. However, the governor said this month he wanted to meet with Democrats to find shared agenda items.
"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 could face a recall election next year, told the Times.
The more cynical said Walker was trying to tamp down prospects of a recall election.
"It's all PR -- none of it is substantive," Mark Miller, the Democrats' leader in the Wisconsin state Senate, said before Walker had what has been called by some as a "cordial" meeting with Democratic leaders last week.
After Walker proposed the public union limits in February, the minority Senate Democrats fled the state to try to block a vote on the measure that eventually passed without them. Nine Senate members -- three Democrats and six Republicans -- faced recall elections during the summer. Results saw Democrats pick up two seats and trim the Republican majority to 17-16.
In Columbus, Democrats and union leaders were in an uproar when Republican Gov. John Kasich and the Republican-controlled Legislature pushed through a law that also would limit the rights of public workers to bargain collectively. However, Democrats and union leaders, operating as the group We Are Ohio, collected more than 900,000 valid signatures to put the law to a vote in a referendum in November.
Last week, Kasich and Republican statehouse leaders sent a letter to union organizers, seeking a meeting to discuss a compromise, the Times said.
"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.
"We ought to get to the table and we ought to talk about it," Kasich told reporters Friday.
"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. "If they wanted to get along, they probably should have tried to during the legislative process instead of locking people out."
Notable deaths of 2014 [PHOTOS]