CARSON CITY, Nev. — When Republican governors in November gathered in Las Vegas to discuss how to recover from their party's latest electoral drubbing, the popular GOP governor of Nevada wasn't there.

Instead, Brian Sandoval was in Washington, D.C., meeting with Obama administration officials to seal the deal that made him the first Republican governor to expand Medicaid as part of the president's health care initiative.

It was part of the pragmatic, centrist, low-key approach that has kept Sandoval popular in a Democratic-trending state and makes him the heavy favorite in his re-election bid next year.

With all the hand-wringing about the future of the GOP, the party has an often-overlooked strength: popular governors like Sandoval who run most of the states in the nation, testing new policies, winning credit for the economic recovery and building records and expertise for possible runs at national office.

Partly due to the party's dominance in the 2010 election, Republicans hold 30 of the nation's 50 governorships.

"The larger the electoral arena, the worse the Republicans seem to do," said Eric Herzik, a political science professor at the University of Nevada, Reno, noting the GOP has lost the popular vote in five of the last six presidential elections and blown a number of high-profile races.

"The one electoral arena that the Republicans have done fairly well in are the governorships," he said.

The 2010 wave ushered in a number of envelope-pushing conservatives. Some, like Florida's Rick Scott and Pennsylvania's Tom Corbett, are long-shots for re-election while others like Wisconsin's Scott Walker or Ohio's John Kasich have weathered early rough patches and are now doing well in the polls.

Sandoval offers a contrasting approach.

"He doesn't get boxed in or pinned down by labels. He's someone who's willing to set aside traditional boundaries if it's going to solve problems," said Greg Ferraro, a longtime Sandoval friend and adviser. "To me, he's the kind of Republican that's going to rebuild the party."

Growing numbers of migrants from the coasts and an expanding immigrant population have steadily pushed Nevada into the Democrats' column in presidential elections. But Sandoval has helped act as a GOP bulwark at the state level. He vetoed a bill to expand background checks for gun purchases as well as another to expand the period for voter registration and nixed a law to place calorie counts on chain restaurant menus.

He is so popular that Democrats have yet to field a challenger, and most analysts predict he will be handily re-elected.

But many of the things that have endeared Sandoval to Nevada voters would make him radioactive among the activists and interest groups who dominate national Republican politics. He supports abortion rights. Although he has refused to approve new taxes, he has twice extended what were supposed to be temporary taxes totaling more than $620 million.

This month, Sandoval signed a bill granting cards that permit driving to people in the country illegally.

"He's got a nice smile, a sunny disposition," said Chuck Muth, president of the Nevada conservative group Citizen Outreach and one of Sandoval's critics from the right. "But that's not something that's going to carry him very far if he ever gets into a competitive primary."

Sandoval had previously served as a state legislator and Nevada's attorney general and had a comfortable position as a federal judge when he agreed to run for governor in 2010. The incumbent, Republican Jim Gibbons, was badly tarred by a painfully public divorce case that included allegations of infidelity. Sandoval ousted him in the Republican primary and easily beat Rory Reid, son of U.S. Senate Majority Leader Harry Reid, in the general election.

He is one of two Hispanic GOP governors elected that year, and he co-chairs a task force with his New Mexico counterpart, Susana Martinez, to recruit more Hispanic Republican candidates. But Sandoval only won 33 percent of the Hispanic vote, just three percentage points higher than Sharron Angle, the Republican challenger to Sen. Reid who campaigned on her stance on illegal immigration.

Sandoval is a halting public speaker and cautious politician. He frustrated many Nevada Republicans by only giving lukewarm support to his party's nominee, Mitt Romney, in the 2012 presidential election.

In many states, the governor has unrivaled power and ability to set the agenda. That's certainly true in Nevada, where the legislature meets for 120 days every two years. In the 2013 regular session, Sandoval came out on top, his $6.6 billion general fund budget proposal left mostly intact thanks to a GOP minority in both chambers that kept Democrats from a two-thirds vote margin needed to raises taxes.

But Sandoval came under criticism from both the right and left when just hours after the June 3 midnight deadline, he called lawmakers back into special session to act on five measures that died in the final hectic minutes — including a sales tax increase in Clark County, where Vegas is located, to fund more police officers.

The Nevada Policy Research Institute, a conservative think tank, chided him for pushing the sales tax bill while abandoning education reforms that were rejected by Democrats.

Liberals also derided him for the special session, saying he should have pursued more tax hikes.

Sandoval also took heat earlier this year after a mentally ill man hospitalized at a Las Vegas psychiatric hospital was given a one-way bus ticket to Sacramento, Calif., where he knew no one. It prompted a weekslong investigation by The Sacramento Bee about "patient dumping." Sandoval eventually fired two staffers and ordered an independent review of practices at the hospital.

The American Civil Liberties Union filed a federal civil rights suit this week on behalf of one patient, and city attorneys in two California cities have criminal investigations underway.

There is already speculation in Nevada that Sandoval, if re-elected, could challenge Reid in 2016, setting up a clash of the state's political titans. Reid and his hard-edged operatives have been relatively polite in discussing the governor, and some Democrats clearly respect Sandoval.

Billy Vassiliadis, a veteran Democratic operative, said the governor's low-key, bipartisan demeanor is a clear asset, but it remains to be seen whether that approach would resonate with the GOP's more aggressive, national approach.

"There's an evolution happening in the Republican Party that will largely determine whether a more moderate Republican like Brian Sandoval could stand on a national stage," he said.