The White House declined to comment on when President Obama would nominate a new commissioner for Social Security. He still is filling out his second-term Cabinet.
Since January, Obama has made 92 nominations, according to White House figures. Thirteen have received Senate votes.
The judges said they have been "scapegoated" by the agency's senior management for the backlog of cases. "Instead of attacking the underlying reality of the delays — more claims and failure to allocate adequate resources — the SSA has imposed an illegal production quota," the lawsuit said.
The judges allege the agency imposed a quota by establishing benchmarks in 2007 that allotted the judges a certain number of days for each stage of their evaluation process.
Judges who haven't met the workload expectation have been subjected to reprimands, "counseling," and "threats and intimidation," they said in the lawsuit.
Frye said the judges and the agency should be working toward a common goal: "To ensure due process, protect the trust fund and bring justice to the American people."
Baltimore Sun Washington correspondent John Fritze contributed to this article.