Barbara Honegger, the political appointee who labeled as "a sham" the Reagan administration's alternative program for the Equal Rights Amendment, yesterday resigned from her $36,000-a-year job, according to Justice Department spokesmen.

The spokesmen did not make available a copy of the letter of resignation, and Honegger could not be reached for comment. But presidential spokesman Larry Speakes said in Los Angeles that she "submitted the resignation quite on her own."

In an article that appeared in the opinion pages of The Washington Post Sunday, Honneger wrote that President Reagan has "reneged on his commitment" to find and change federal and state laws that discriminate against women.

The controversy comes at a time when administration officals have made a top political priority of trying to close the so-called "gender gap," launching a public relations offensive to increase Reagan's support among women.

Both Republican and private pollsters have shown that women tend to disapprove of Reagan in far greater numbers than men, a trend that threatens his chances of carrying some key southern states if he seeks re-election.

Since the 1980 campaign Reagan has opposed efforts to enact an Equal Rights Amendment. Instead, he appointed an Interagency Task Force on Women's Legal Equity to correct discriminatory aspects of existing federal law.

Honegger's article in The Post identifed her as "project director" of a Justice Department group providing the task force with a list of laws containing discriminatory provisions. Although her group had submitted three "quarterly reports" to the White House, she said, "not one single law has been changed."

The article drew a general denial from Speakes in Los Angeles, where Reagan is vacationing. Speakes said the president had read the article and believed it was "just not true." Speakes said of the article that "the impressions were more erroneous than the facts."

The tone of the White House response was mild compared with denunciations yesterday from the Justice Department officials. In the hours after Honegger made appearances on several national television news programs, various Justice officials characterized her as a self-aggrandizer preoccupied with titles, and as a woman piqued at her inability to get a new job with the administration as her temporary appointment was running out.

Justice spokesman Thomas P. DeCair called Honegger a "low-level munchkin," and denied that a separate "gender discrimination agency review group" ever existed or that Honegger had headed it.

"There is no group or board; there is no separate entity of any kind," DeCair said. "She is not the project director . . . . She was not the project director."

He added that "I find it absolutely incredible that The Washington Post would run that piece from a low-level munchkin."

DeCair also accused The Post of failing to check Honegger's credentials with Justice ahead of time.

Meg Greenfield, editorial page editor of The Post, responded, "We did check it out with people at Justice and elsewhere. We checked documentary evidence also . . . . We were satisfied she had been doing the work she said she was doing. So far as I know, the administration has not challenged her account in the article, which we also did a lot to check."

In a June 17 letter on Justice Department letterhead, Stewart Oneglia wrote a general job recommendation for Honegger, whose Schedule C politcal appointment was to expire Sept. 30. In the letter, Oneglia--who serves as chief of the coordination and review section of Justice's Civil Rights Division and was Honegger's immediate supervisor--said Honegger had drafted the executive order creating the interagency task force and giving Justice the job of reviewing "laws, regulations, policies and practices" which discriminate on the basis of sex.

The letter said she "then moved to the Department of Justice to implement the order as project director of the attorney general's review."

Told of the letter, DeCair said, "I'm sure bosses write nice letters for departing employes all the time . . . . I don't really care."