These state leaders are offering greater cooperation on health care and skipping the tough talk on immigration, taking a cue from voters who in last November's election expressed their opposition to partisan gridlock in Washington.
For many governors, the new approach reflects not just the specific needs of their states but also the realities of the political calendar: Nearly two dozen GOP governors elected in 2009 and 2010 could face the voters again.
"People may agree or disagree with my position on this social issue or that social issue, but as long as I'm not rubbing it in their face all the time and instead talking about jobs and balancing the budget in a way that's relevant to their lives, that's where the real focal point is," said Wisconsin Gov. Scott Walker in an interview during the weekend's National Governors Association meeting.
Walker, who survived a high-profile union-led recall challenge last year, said his marching orders are clear: "We've got to be relevant."
The shift is most pronounced on health care, where seven states led by Republican governors are pushing to expand their Medicaid program under Obama's health care law. Such a move once was considered anathema in the party.
Under the terms of the deal, Washington pays the full cost of the expansion for the first three years, gradually phasing down to 90 percent. The changes would cover millions of low-income people, mostly uninsured adults.
Last week, Florida Gov. Rick Scott, a former health care executive who rallied opposition to the law, became the latest Republican to make the move. He said the Supreme Court's decision in the health care case and Obama's re-election had made the president's "health care mandates the law of the land."
Scott's Medicaid decision followed similar pivots by Govs. John Kasich of Ohio and Rick Snyder of Michigan. Each leads a state that Obama won last year and each has struggled with approval ratings below 50 percent.
With Obama and Republicans in Congress at loggerheads over $85 billion in mandatory spending cuts set to take place Friday, governors from both parties are encouraging a deal that would delay cuts that could hurt their local economies.
GOP Gov. Bobby Jindal of Louisiana has opposed the Medicaid expansion and the health overhaul. On Sunday, he suggested on NBC's "Meet the Press" that Congress could delay that expansion and the establishment of health care exchanges under the law and save billions without "even cutting a program that's started yet—just delay it."
On CBS's "Face the Nation," Republican Gov. Bob McDonnell of Virginia joined with Democratic Gov. Martin O'Malley of Maryland to call for Congress to prevent impending defense cuts that would hit their states hard.
Another case study can be found in Arizona, where Gov. Jan Brewer was labeled a conservative firebrand in 2010 for supporting her state's crackdown on illegal immigration. Now, halfway through her first term, she's softened her tone on immigration as Obama and Congress pursue a comprehensive overhaul.
In an interview, Brewer said it was easy to hold fast to ideological convictions as a candidate, but when "you have to govern for the whole state you have to be very pragmatic with your decision-making. You govern. And you have to make the trains run and the lights work and make tough decisions. You can't please everybody all the time, but you have to be much more pragmatic."
Pragmatism hasn't always been found in abundance.
During Obama's first term, Republicans fought the health overhaul in court and outside. Others refused federal money to develop high-speed rail lines or pressed to undermine the power of unions. During his campaign for governor in 2010, Scott frequently called Obama's health care plan a "job-killer" that would hurt Florida.
Walker drew the ire of Democrats when he successfully pushed for restrictions to collective bargaining rights for public sector workers. That led unions and Democrats to push for his recall. Walker survived the recall election, but emerged with a change in tone and a focus on issues such as improving roads and bridges, education and workforce development.
"The big thing I keep pushing is relevance," he said. "Where we connect with voters, and where we connect now that we're in office, is by continuing to talk about and deal with things that are relevant in peoples' lives."
Many Republicans say the approach simply reflects the need to tackle problems that are most relevant to their states.
Oklahoma Gov. Mary Fallin noted that most of the 30 GOP governors have decided against expanding Medicaid and rejected calls by the Obama administration to create their own state exchanges under the health law.
"It's not moderation and nothing has changed," said Nick Ayers, the former executive director of the Republican Governors Association. "There's still uniformity in opposition to (Obama's) domestic policy agenda, particularly on health care. What's changed is now they're actually stuck with dealing with making the best decision based on a bad set of options."
Democrats contend it will be more difficult for Republicans to adhere to conservative GOP orthodoxy prevalent in Congress and win re-election next year.
Vermont Gov. Peter Shumlin, who leads the Democratic Governors Association, said Scott's decision "was less about an ideological transformation on Rick Scott's part than it was a 30 percent approval rating that will certainly get your attention as a governor."