WASHINGTON – Brian Sandoval, the centrist Republican governor of Nevada, is being vetted by the White House for a possible nomination to the Supreme Court, according to two people familiar with the process.

Sandoval is increasingly viewed by some key Democrats as perhaps the only nominee President Barack Obama could select who would be able to break a Republican blockade in the Senate.

Senate Majority Leader Mitch McConnell, R-Kentucky, on Tuesday pledged “no action” on any Supreme Court nomination before November’s election, saying the decision ought to be left to the next president.

The White House declined to comment Wednesday for this story. White House press secretary Josh Earnest has emphasized in recent days that the president has not arrived at a short list of potential nominees.

On Wednesday morning, Obama stated again he would “do his job” and nominate someone to fill the court vacancy. Referring to McConnell and Senate Republicans, he said: “I recognize the politics are hard for them, because the easier thing to do is to give in to the most extreme voices within their party and stand pat and do nothing.”

Obama also predicted that the Republican position “may evolve” if the public believes his nominee is “very well qualified.”

“I don’t expect Mitch McConnell to say that is the case today. I don’t expect any member of the Republican caucus to stick their head out at the moment and say that. But let’s see how the public responds to the nominee that we put forward,” the president said.

The nomination of a GOP governor — albeit one with a bipartisan record — could break that resolve.

Sandoval met Monday with Senate Minority Leader Harry Reid, a fellow Nevadan with whom he enjoys cordial relations.

A person familiar with the conversation said that while Sandoval told Reid he had not made a final decision on whether he would accept a Supreme Court nomination, he would allow the vetting process to move forward. Another person in Nevada familiar with the process confirmed that the process is underway.

Sandoval could not immediately be reached for comment.

It is unclear how many potential nominees are undergoing White House vetting for the high court vacancy left by Justice Antonin Scalia’s death. Obama was seen last week carrying a thick binder of materials on potential picks to review.

Obama outlined his thinking in a guest posting on SCOTUSblog Wednesday: “A sterling record. A deep respect for the judiciary’s role. An understanding of the way the world really works. That’s what I’m considering as I fulfill my constitutional duty to appoint a judge to our highest court.”

Some Democrats believe that nominating Sandoval could fracture the front of Republican opposition and force McConnell to take up the nomination in this contentious election year. It would also put on the spot a handful of Senate Republicans who are up for reelection in blue states in November.

The Senate unanimously confirmed Sandoval as a district court judge in 2005 after he was nominated by President George W. Bush. The Nevada Republican stepped down from the bench in 2009 to run for governor and is now counted among the most popular governors in the nation. He also represents a swing state with a heavy concentration of Latinos who will be important in the presidential race.

But at least one Republican — Sen. Orrin Hatch, who is from neighboring Utah — said nominating Sandoval wouldn’t change his mind not to act on Obama’s candidate.

“I think very highly of him,” Hatch said. Asked if Sandoval was qualified to serve on the court, Hatch said, “I wouldn’t make that judgment now.”

One Republican who is considered likely to support Sandoval if nominated is Nevada’s junior senator, Dean Heller.

Heller suggested in a statement last week that the “chances of approving a new nominee are slim” but he did not discourage Obama from putting forth a nominee.

“[W]ho knows, maybe it’ll be a Nevadan,” he said — a comment widely interpreted as signaling his support for Sandoval.

But nominating Sandoval would carry risks for Obama. Sandoval is aligned with Democrats on some key issues, including abortion rights and the environment. As governor, he has moved to implement the Affordable Care Act, and has said he considers same-sex marriage to be a settled issue.

But Sandoval is not seen as labor-friendly — potentially alienating a swath of the Democratic base. His legal credentials are also lacking compared to some of the other names under consideration who are mainly sitting federal judges.

A Senate confirmation of Sandoval through this year could deny a Democratic successor to Obama, whether Hillary Clinton or Bernie Sanders, the opportunity to nominate a more orthodox liberal to the court and cement an ideological shift in its jurisprudence.

Asked by The Morning Consult in a brief interview Saturday about a potential nomination, Sandoval said, “It would be a privilege,” calling the Supreme Court “the essence of justice in this country.”

In a parallel storyline that could significantly affect any confirmation battle if Sandoval is nominated, Reid and Sandoval have long had a symbiotic political relationship that sometimes defied logic.

Elected as the state’s attorney general in 2002, Sandoval quickly became one of the more popular Republicans in Nevada. In early 2005, Reid began pushing the governor to take a seat on the state’s U.S. District Court — a move that political insiders viewed as a savvy bid by Reid to take Sandoval off the potential field of rivals who might run against him in his 2010 Senate race.

Sandoval was nominated and then confirmed as a federal judge in October 2005 without any opposition, clearing the Senate Judiciary Committee by a voice vote and then winning full Senate confirmation by an 89-0 vote. Four years later, as then-Republican Gov. Jim Gibbons’s popularity was imploding amid a variety of scandals, the state’s GOP elites convinced Sandoval to bail them out and challenge Gibbons in a June 2010 primary.

Sandoval ousted Gibbons and then in the November 2010 general election, he routed Rory Reid, 53 percent to 41 percent, knocking off the Senate leader’s son.

Harry Reid — who is retiring in 2016 — won his own re-election that year in a bid that left some surprised by the senator’s seeming reluctance to help boost his son’s campaign against Sandoval.

As governor, Sandoval alienated many conservatives by accepting the Medicaid expansion that was a cornerstone of Obama’s Affordable Care Act, and one of his recent budgets, passed over the opposition of many Republicans in the legislature, included tax hikes designed to boost funding for the state’s notoriously under-performing public schools.

As the 2016 election cycle got underway a year ago, Republicans in Washington set their sights on Sandoval as their top recruit to try to challenge Reid. However, in public and private, the governor made clear that he had little interest in running in a competitive primary and then challenging Reid in the general election. Reid is retiring in 2016, leaving a competitive open Senate seat behind him.

All this occurred while Reid repeatedly praised Sandoval for his positions on health-care, taxes and education, and when the Senate leader announced in late March 2015 that he would not run for re-election, Sandoval returned the favor by praising his onetime patron for the federal judgeship.

“From humble beginnings in Searchlight to the United States Senate, Senator Reid’s story is one that represents the Nevada and American dream,” Sandoval said.

The Washington Post’s Paul Kane contributed to this report.