After The Washington Post published news of Sandoval’s consideration Wednesday, GOP leaders insisted that Obama nominating a Republican would make no difference.

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Senate Majority Leader Mitch McConnell (R-Ky.), who on Tuesday pledged “no action” on any Supreme Court nomination before the election, said in a statement that the nominee “will be determined by whoever wins the presidency in the fall.”

The No. 2 Senate Republican leader, Majority Whip John Cornyn of Texas, said likewise: “This is not about the personality.”

White House press secretary Josh Earnest told reporters Wednesday he would not comment specifically on whether the administration was considering Sandoval because he did not want “to get into a rhythm of responding” to every report on a potential nominee. But he said that Obama was committed to finding “the best person to fill the vacancy at the Supreme Court,” regardless of party.

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“The president’s focused on criteria that, frankly, is more important, and that is that individual’s qualifications, and their experience and their view of the law,” Earnest said. “That will take precedence over any sort of political consideration.”

Sandoval would represent an unconventional pick for the president, a former constitutional law professor who has prized prestigious law pedigrees and extensive legal backgrounds in the jurists he has previously selected for the Court. While the selection of a Republican could heighten the political pressure on Senate GOP leaders, it could also alienate the Democratic base and runs counter to Obama’s emphasis on taking a long view of who deserves to sit on the nation’s highest court.

Speaking to reporters last week, the president said he planned to select someone with extraordinary legal credentials. “We’re going to find somebody who is has an outstanding legal mind, somebody who cares deeply about our democracy and cares about rule of law,” he said.

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A Sandoval spokesman, Mari St. Martin, said Wednesday, “Neither Governor Sandoval nor his staff has been contacted by or talked to the Obama administration regarding any potential vetting for the vacancy on the U.S. Supreme Court.”

It is clear, however, that Senate Minority Leader Harry M. Reid, a fellow Nevadan with whom Sandoval enjoys cordial relations, is playing a key role as intermediary. While visiting Washington for a meeting of the National Governors Association, Sandoval met with Reid in his Capitol office Monday.

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 it is underway.

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Asked about a potential nomination on Saturday, Sandoval told the Morning Consult, “It would be a privilege.” He called the Supreme Court “the essence of justice in this country.”

In a Wednesday interview with CNN, Reid said he would endorse Sandoval for the nomination. “I don’t pick the justices, but I know if he were picked, I would support the man,” he said. “He’s a good person, has a great record, and has been a tremendously good governor in spite of having to deal with some very big problems there.”

But in subsequent remarks to The Post, Reid tempered his praise and said he was “not pushing it with the White House” and was “just responding to people.”

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“He was a good judge. He’s been a very excellent governor. I like him very much. I would support him,” Reid said of Sandoval. “I would rather we had somebody a little more progressive…. I’ll do what I can, but I’m not pushing his name.”

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

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As the standoff continued with Senate Republicans, Obama reiterated Wednesday morning that he intended to “do his job” by nominating a candidate during the remaining months of his presidency.

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Referring to McConnell and Senate Republicans on Wednesday morning, Obama 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.”

But he 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.

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Some Democrats see a Sandoval nomination as the best opportunity to 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.

Several Republican members of the Judiciary Committee, which is charged with considering a Supreme Court nominee, said Wednesday that it would not matter if Obama picked a Republican.

“The short answer is no, it doesn’t change anything,” said Sen. Mike Lee (R-Utah).

But some Republican senators acknowledged a Sandoval pick would put GOP senators in a tough spot politically.

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“This is one reason why I have not wanted to shut the door on considering a nominee,” said Sen. Susan Collins (Maine), one of two Senate Republicans who is at least open to a confirmation hearing. “We may well be sent a nominee who is deserving of thorough vetting and consideration.”

Another Republican senator aligned with the GOP court blockade, who spoke on the condition of anonymity to speak frankly, said a Sandoval nomination would “mix it up” for Republicans. But the lawmaker also said he doubted that Democrats would unite behind Sandoval.

Nominating Sandoval would carry clear political 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.

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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. And he initially called the landmark health-care law “unconstitutional,” signing onto a brief in 2012 challenging the constitutionality of the measure’s individual mandate. The Supreme Court ultimately rejected that argument, and upheld the law.

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.

Liberal activist groups quickly registered their displeasure with the idea of a Justice Sandoval. Charles Chamberlain, executive director of Democracy for America, said in a statement it was “downright absurd that President Obama would risk his legacy by appointing another anti-labor Republican like Brian Sandoval to an already overwhelmingly pro-big-business Supreme Court.”

“Nominating someone like Sandoval would not only prevent grass-roots organizations like DFA from supporting the president in this nomination fight, it could lead us to actively encouraging Senate Democrats to oppose his appointment,” Chamberlain said.

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.

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.

In a parallel story line, 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 Sandoval to take a seat on the state’s U.S. District Court – a move that political insiders viewed as a savvy one to take Sandoval off the potential field of rivals who might run against Reid 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 persuaded Sandoval to bail them out and challenge Gibbons in a June 2010 primary.

Sandoval ousted Gibbons — and in November 2010, 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 reelection 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. 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 underperforming public schools.

As the 2016 election cycle got underway a year ago, Washington Republicans 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 Democratic leader announced in late March 2015 that he would not run for reelection, Sandoval returned the favor by praising his one-time 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.