President Carter nominated D.C. Superior Court Judge Norma Holloway Johnson yesterday to a seat on the federal court here, ending months of intense lobbying by supporters who were concerned that she would not get White house approval for the job because of opposition from some members of the bar.

If her nomination is confirmed by the Senate, Johnson, 47, a local court judge since 1970, would be the first black woman appointed to the U.S. District Court for the District of Columbia. She would replace Judge George L. Hart Jr., who has taken the semi-retired status of a senior judge.

After it became known last fall that Johnson was the Carter administration's choice for the seat, various concerns were raised buy some bar members about Johnson's judicial temperament and experience.

After a report about the concerns was published in a legal journal, and rumors began spreading that her nomination might be in jeopardy, an unusally strong lobbying effort began in her behalf.

Much of the concern focused on an American Bar Association judicial screening committee, whose approval is considered critical to any federal court nominee. It was learned that a majority of the committee eventually rated Johnson as "qualified" for the job, the lowest rating for a judicial candidate.

Various sources said yesterday that Johnson, a former Justice Department lawyer and assistant D.C. Corporation Counsel, had strong backing from local trial and appellate judges, influential lawyers and others who appeared before her in the local court. These sources said the opposition to Johnson came from the public interest bar and defense lawyers.

"Norma's support for the judgeship existed all along," one local lawyer said. Concerns arose when her nomination appeared to be delayed, this lawyer said and the reasons for the delay often were unclear to members of the bar.

"She can be a very stern lady, but she can also be the paragon of compassion and concern at times," the lawyer said. "I think it depends on the issue before her at the time."

Another source said that Johnson during her early years on the local bench, developed a reputation for being "strong-willed and austere . . . which may or may not be true."

That reputation, this lawyer said, followed Johnson through her nomination to the federal bench.

"She's tough, she's been tough," this lawyer said.

Once information began circulating that Johnson's nomination was being questioned, the National Bar Association, which represents the nation's black lawyers, conducted a survey of 95 local lawyers and judges for an evaluation of Johnson's judicial qualifications. A lengthy report then was submitted to Attorney General Benjamin R. Civiletti and President Carter, according to the association's executive director, John Crump.

As a result of the survey, the association rated Johnson as "highly qualified" for nomination to the federal court, the second-highest ranking it gives to judicial candidates. The survey was conducted by Ricardo Urbina, an associate professor at Howard University Law School and director of Howard's Criminal Justice Program, and John Mercer, the program's supervising attorney.

According to Crump, similar surveys have been conducted by the association on other judicial nominees, whether or not there are reports of problems with their nominations.

He said the association "went to work to see what the real issues were" after an unfavorable report was published in a legal journal and "rumblings from the ABA."

One issue that sources said was raised by the ABA was a report that Johnson had a long tenure in the Superior Court's juvenile division. The concern was whether this was an indication that Johnson did not have the broad experience needed for the federal court.

Urbina said, however, that the survey showed that Johnson's assignment to juvenile court was not unusually long. Moreover, he said, she was the only female Superior Court judge to be assigned to handle complex civil litigation.

Johnson's judicial temperment also was a focus of the association's study, Urbina said. He recalled one comment that Johnson was a "firm and austere" judge but that her manner had never interfered with the rights of anyone who appeared in her courtroom.

It was learned yesterday that Johnson's supporters telephoned members of the American Bar Association's Board of Governors to lobby in her behalf. Once the ABA gave Johnson a qualified rating, the effort in her support appeared to move to the White House.

Lenore Cameron, the president of the Washington chapter of the women's division of the National Bar Association, said members wrote letters for Johnson, "talked to different people" in her behalf and telephoned the White House.

Sources said the White House later quietly put out assurances that Carter would nominate Johnson to the federal bench.