WASHINGTON — At the heart of the rancorous showdown between Senate Republicans and Democrats over President Obama’s blocked political appointments is an unglamorous federal agency that polices labor practices and that has, for Republicans, become a reviled symbol of the Obama administration’s bureaucratic overreach.

The agency, the National Labor Relations Board, has functioned without a full slate of five members, and with its existing appointees in legal limbo, for Mr. Obama’s entire presidency.

This chronic disarray, experts say, has left the 80-year-old agency rudderless, throwing into doubt dozens of rulings on the nation’s thorniest labor disputes.

Republicans have never been enamored of the board, generally viewing it as a New Deal creation to foster unionism.

But their anger spiked in 2011 when the board’s acting general counsel filed a case against Boeing, asserting that its plan to open an aircraft assembly plant in South Carolina constituted illegal retaliation against the company’s workers in Washington State for repeatedly going on strike.

Although Boeing eventually settled the case with the board, Republicans accused it of discriminating against states in the South that were attracting investment from more heavily unionized states.

Senator Lindsey Graham, Republican of South Carolina, denounced the agency as “the Grim Reaper of job creation,” and said he would place an indefinite hold on labor board nominations to prevent it from making any major decisions.

“The N.L.R.B. is a four-letter word in South Carolina,” Mr. Graham said in a telephone interview on Monday, explaining his refusal to allow a vote on Mr. Obama’s nominees. “I do understand that they need to exist, but they’ve sort of been a rogue organization.”

With Washington in an era of extreme partisanship, it is perhaps unsurprising that Republicans, supported by their business allies, have declared war on the agency that is linked most closely to corporate America’s longtime nemesis, organized labor.

For some in the labor movement, the Republicans’ anger toward the board is less about any specific legal action than a wholesale assault on the New Deal-era laws that underpin its work.

“There’s a breakdown of what used to be a consensus that the workers should have a right to organize, that this should be protected by the government, and that collective bargaining is a good thing for the country,” said Craig Becker, a labor lawyer and former member of the labor board who is now general counsel of the A.F.L.-C.I.O.

The politics goes both ways, as Mr. Becker’s experience demonstrates. Senate Democrats refused to confirm some of President George W. Bush’s nominees to the board in his final year in office, and Republicans responded in kind when Mr. Obama nominated Mr. Becker, who was then an outside lawyer for the A.F.L.-C.I.O. and Service Employees International Union.

With Mr. Becker’s nomination hung up, Mr. Obama named him to be the board March 2010 when Congress was in recess.

Republicans dug in when they refused to confirm Mr. Obama’s subsequent nominees. In January 2012, the president made three more recess appointments to the board.

But in January of this year, a federal appeals court ruled that those appointments were unconstitutional. The board is likely to shrink to just two members next month, leaving it without the quorum of three needed to conduct business like enforcing its rulings, or those of its offices across the country.

“The situation we’re seeing now is really unprecedented,” said David L. Gregory, a professor of labor law at St. John’s University. “There was a period of chronic vacancies that was as much the fault of the Democrats as the Republicans. But we really haven’t seen a showdown like this in modern history.” The White House reiterated Monday that Republicans were “needlessly and systematically” obstructing the president’s nominees, arguing that he had put forward a full bipartisan set of candidates in April.

“Republicans want to make this an ideological fight in an effort to dismantle the agency,” said Eric Schultz, a White House spokesman. “If the Senate fails to act, the board will lose a quorum in August and be unable to function, which is exactly what Republicans are seeking.”

In addition to the Boeing case, Republicans complain that the board has ordered businesses to post notices informing employees of their right to unionize, and has issued new rules to streamline and speed up unionization elections — making it easier, in theory, for workers to organize.

Randel K. Johnson, senior vice president for labor issues at the U.S. Chamber of Commerce, said the N.L.R.B. was far too chummy with organized labor. “We think this labor board is more liberal than virtually any prior board, and they were improperly appointed to begin with,” he said.

Some labor experts say Republicans are also motivated by simple political calculations, confronted by a Democratic president who is proposing nominees with close ties to labor.

“Republicans like to go after unions because unions support Democrats,” said Benjamin Sachs, a labor law professor at Harvard.

The agency, he said, has played an important role by intervening to protect workers’ rights to unionize — punishing employers that illegally fire workers for supporting a union or that unlawfully threaten to close a factory if employees vote to form a union.

The board has jurisdiction over industries with about 100 million employees, including seven million who are union members. As union membership has dwindled, the board has asserted its power to protect nonunion workers, issuing rules that make it illegal for companies to punish workers for communicating on Facebook or by e-mail about their wages or bosses.

“Whether you already have a union, or you’re trying to form a union, or you’re having a conversation with a co-worker about problems you face on the job, the N.L.R.B. is the only place you can go to protect your rights at work,” said Larry Cohen, president of the Communications Workers of America.