WASHINGTON (AP) — Many Republican governors who worked to thwart much of President Barack Obama's first-term agenda are shifting gears and softening their rhetoric now that his run was extended for four more years and they're facing their own re-election.

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.