Some District judges have found themselves in the unusual position of envying the city’s teachers, firefighters and garbage collectors. Those jobs come with something not currently available to those who wear robes to work: the ability to join a union.

Now a group of city administrative law judges is seeking to organize for the first time, and the months-long effort — taking place over the strenuous objections of the judges’ supervisor — has generated frustration among union advocates who think Mayor Vincent C. Gray has failed to match his pro-labor rhetoric with action.

“We’re in Washington, D.C., and we’re seeing the kind of stuff that has gone on in Wisconsin, the kind of stuff that’s gone on in Michigan, the kind of stuff that’s gone on in Indiana,” said Paul Shearon, secretary-treasurer of the International Federation of Professional and Technical Engineers, the union that is helping the judges in the Office of Administrative Hearings organize.

The reference to the recent union-related measures by Republican governors and legislators in traditionally labor-friendly states might be exaggerated. But the Gray administration’s top labor relations officials initially opposed the judges’ attempts to organize, and although they have since withdrawn from the case, the agency’s chief judge has hired a high-powered private law firm to keep fighting.

The organizers insist that Gray, under D.C. law, can step in and recognize the union. That is a request they have pressed in recent months in meetings with City Administrator Allen Y. Lew, House Del. Eleanor Holmes Norton (D), D.C. Council Chairman Phil Mendelson (D) and Gray himself.

D.C. Mayor Vincent Gray (Sarah L. Voisin/The Washington Post)

But Gray (D) has declined to do so. On Wednesday, lawyers from the Office of the Attorney General filed a legal brief in support of the judges’ right to organize. The administration is leaving it to a city employee labor-relations board to hear the case and rule on the matter.

The city has “literally opposed everything, procedurally and substantively,” until Wednesday’s brief, Shearon said. “We believe the facts are clear.”

Gray spokesman Pedro Ribeiro declined to comment on the judges’ efforts, citing the pending litigation. As a general matter, he said, “The mayor is in support of collective bargaining.”

The tensions within the Office of Administrative Hearings stretch back more than a year and were publicly aired last June, when 15 judges signed a letter addressed to Mendelson accusing OAH Chief Administrative Law Judge Mary Oates Walker of a “lack of transparency, predictability, and competence.”

The letter, among other things, cited a “chilled work environment that is unduly stressful, demeaning, and counterproductive to overall operations” and “unprofessional, erratic, and at times demeaning” treatment of staff by Walker.

A month later, the judges filed papers seeking to form a union. The judges leading the organizing effort declined to comment, directing questions to the IFPTE organizers.

Walker referred questions on the organizing effort to her agency’s private attorneys, from the Venable law firm, hired in December under the quasi-independent agency’s legal authority. In an interview last June, she characterized the complaints as the result of management changes intended to make the office more productive. “A number of employees are obviously resistant to those changes,” she said.

In February testimony to the D.C. Council, Walker touted “noteworthy” progress in the office’s productivity under her management, saying it “resolved more cases, more efficiently in fiscal year 2012 than in any year since the agency began operations in 2004.”

Kenneth Slaughter, a Venable attorney representing the agency, said the judges are appealing to the media and the public because they are “weak on the law.”

The key question at stake is whether the line judges are supervisors or managers who would thus be prohibited from unionizing under the District’s employment law. The agency has argued that they are essentially managerial, directing the activities of paralegals, clerks and other agency support staff. But judges said they are not — the staffers do not report to them directly, they said, but are supervised by the chief judge and shared among all the judges.

Administrative law judges, who handle a variety of disputes involving government agencies, have unionized in other places. More than 1,400 federal administrative law judges handling immigration, Social Security and Health and Human Services matters are members of IFPTE-affiliated associations, and judges in at least five states also have organized. Many District lawyers — who, like the judges, share legal support staff — have long been unionized.

The Office of Administrative Hearings employs 29 judges, including Walker, a deputy chief, and five “principal” judges. Shearon said about three-fourths of the line judges have signed organizing cards; to hold an election, 30 percent is necessary, with a simple majority necessary to have the union recognized.

The organizers said the effort is less about salaries and benefits — line judges make $135,900 plus fringe benefits worth about $25,000 yearly, with pay and tenure governed by city law — and more about having a more formal way to address the workplace matters laid out in the June letter, including performance evaluations, transparency and workload.

The matter is set to go to mediation in late April, but the organizers believe the judges have a right to bargain collectively and have thus far resisted participating.

The dispute is being closely watched by labor leaders in the city, who are concerned that if Walker prevails, other city agencies with similar independent status might break with the mayor to separately negotiate employment matters.

“It would set a very bad precedent,” said Joslyn N. Williams, president of the Metro Washington Council AFL-CIO. “It’s an invitation for other so-called quasi-independent organizations to say they are not covered by the same rules that the rest of the agencies are covered by.”

But Williams, a political supporter of Gray’s, said he did not think the contentious process reflected bad faith on the mayor’s part. “I can understand their anxiety and frustration,” he said of the judges. “But I have been around long enough. I know how long these things can take.”