By Lawrence Hurley

WASHINGTON (Reuters) - Merrick Garland hit an unwanted milestone on Tuesday as the federal appeals court judge's nomination to the U.S. Supreme Court reached its 125th day with no Senate action, tying for the longest pending nomination ever to the high court.

In a move with little precedent in American history, the Republicans who control the Senate have simply refused to take any action on President Barack Obama's nomination of Garland, 63, for a lifetime job on the nation's top court.

Having been nominated on March 16 to replace conservative Justice Antonin Scalia, who died on Feb. 13, Garland, chief judge of the federal appeals court in Washington, has now matched Louis Brandeis for the longest time between nomination and Senate action.

In 1916, the Senate voted to confirm Brandeis, making him America's first Jewish justice.

The U.S. Constitution assigns the Senate the power to confirm the president's nominations to the Supreme Court. The Senate's inaction on Garland has made the court vacancy a key political prize in a presidential election year.

Republicans, hopeful of winning back the White House from the Democrats in the Nov. 8 election, insist that Obama's successor name Scalia's replacement, who could have a lasting effect on the ideological balance of a court now split with four liberals and four conservatives.

Obama has appointed two of the current justices: liberals Elena Kagan and Sonia Sotomayor.

The White House and its allies made another push on Tuesday to highlight Republican intransigence.

"Now, despite Chief Judge Garland's extraordinary qualifications, Republicans in the Senate have refused to do their job, and Chief Judge Garland's nomination has now been pending longer than any Supreme Court nominee in history who's nomination was not otherwise withdrawn," White House spokesman Josh Earnest told reporters.

"Despite his outstanding record and qualifications, Republicans have obstructed Judge Garland’s nomination in a way faced by no other Supreme Court nominee in our nation’s history," added Senate Democratic Leader Harry Reid.

The Senate is on recess until September.

For the rival presidential hopefuls, Republican Donald Trump and Democrat Hillary Clinton, the Supreme Court vacancy is both a political problem and an opportunity.

IDEOLOGICAL BALANCE

In addition to Scalia's replacement, the next president conceivably could nominate as many as three more justices. Three of the court's current eight members already are over age 77. That means Obama's successor could influence the court's ideological direction for decades.

Some conservatives view Trump with suspicion. But the wealthy New York real estate developer has already floated names of conservative potential nominees in a bid to mollify some on the right.

Garland has established a reputation as a centrist in 19 years as an appellate judge. Some liberal Democrats have said Clinton, if elected, could put forth a nominee more liberal than Garland, so Republicans would be smart to approve him before Obama leaves office on Jan. 20.

Such arguments have not swayed Republican Senate Majority Leader Mitch McConnell, who refuses to let Garland come to a vote.

The development most likely to prod Senate action is the result of the presidential election. Some Republican senators have said if Clinton wins, the Senate should confirm Garland in a "lame-duck" post-election session out of fear Clinton would name someone far more liberal. If Clinton wins, she also could renominate Garland upon taking office.

Garland's nomination is unusual because there has been no controversy over his suitability to sit on the Supreme Court, as there have been with some nominees in the past. He is widely respected in the legal community and has been praised by both Democrats and Republicans as a moderate.

The White House tried to persuade Republicans to accept Garland when he was first nominated in March. He met with 61 of the 100 senators. But the effort fizzled, and Republicans largely followed McConnell's lead.

The White House since then has tried to keep the Garland nomination in the public eye, with limited success. Obama wrote an opinion piece in The Wall Street Journal on Monday, pushing for Senate action.

A White House-allied group called the Constitutional Responsibility Project is running a "We Need Nine" campaign that refers to the number of justices on a fully staffed court. It has bought ads in Cleveland, where the Republican presidential nominating convention began on Monday, calling for senators to "do your job" and bring Garland's nomination to a Senate vote.

In the meantime, Garland is nowhere to be seen. His last public appearance was on June 15 when he spoke at an elementary school commencement event in Washington.

When nominated, Garland stepped aside from pending cases before the appeals court where he works. His only official duties now are administrative as the court's chief judge. A court official said Garland will continue to not participate in cases while the nomination is pending.

(For a graphic on how long Supreme Court nominees usually wait click http://fingfx.thomsonreuters.com/gfx/rngs/1/1420/2255/index.html )

(Additional reporting by Richard Cowan; Editing by Kevin Drawbaugh and Will Dunham)