Chief Justice Warren E. Burger said yesterday that the growing workload of the Supreme Court someday may make it "impossible" for the person in his post "to perform his duties well and survive very long."

He made the statement during a 50-minute talk at the final session of a 2 1/2 day conference on "The Role of the Judiciary in America," sponsored by the American Enterprise Institute for Pulic Policy Research at the Washington Hilton Hotel. Former president Ford sat near him at the head table.

As he, some other justices, and various study groups have done over the years, Burger focused on the problems created by a caseload that has more than doubled in the last two decades; on duties he has as chief justice, including those involving the entire federal judiciary, and on possible remedies.

Apparently for the first time yesterday, however, he suggested "the most careful study" of the possibility of creating a post called "circuit judge for administraction" to take over some of the administrative duties in the federal judiciary that the chief justice now handles.

Burger emphasized that the idea is in an exploratory stage, saying that it raises "very, very serious questions," such as who would appoint the judge and what relationship he would have with the chief justice.

He also explicity repudiated reports that he had endorsed creation of a permanent, intermediate national appeals court to handle cases referred to it by the Supreme Court. "I have not at any time endorsed" it, although, he said, he wouldfavor an experiment, possibly for five years, with such a court.

Burger said that hi plea was simply that Congress and others recognize that an overload exists and ponder what should be done about it before "glacial pressures" get out of control.

In this regard, the Carter administration and Sen. Edward M. Kennedy (D-Mass.) are contemplating the introduction next month of a bill for a different kind of new appeals court than Burger and others have discussed: one that would end conflicts among the 11 U.S. courts of appeals by handling all federal civil tax, patent, trademark, and certain other cases.

In addition to relieving the Supreme Court of the need to resolve numerous conflicts among the circuits, the proposal also would ease the caseload of the appellate courts.

Burger cited some bizarre cases to illustrate the desire of many Americans to litigate almost anything. One example involved a student whose complaint was that he had gotten a "D" rather than the "A" he claimed to deserve. Maybe judges should be empowered to penalize lawyers who abuse their "monopoly access" to the courts to bring such cases, Berger remarked.