Drew Days III has been a harried man in recent months. Not only is he one of the key minds behind the administration's developing position in the Allan Bakke "reverse discrimination" case - a position that so far as it is known many of his former civil rights colleagues have difficulty with - but he's also having his consciousness raised on the home front as well.

At 35, Days, the first black assistant attorney general to head any division of the Justice Department in its 187 year history, is coming to grips with the standard Washington dilemma: How to mix job with family life.

Days, who heads the Civil Rights Division, is all cool efficiency and conviviality, however, as he eases into a chair in his office, the former sanctum of the late J. Edgar Hoover. (The FBI director's office is now in the new FBI building.)

"No one asks about Bakke anymore. They all say 'How's my friend Allan?'" laughs Days, about the case that has had him working around the clock for the past several weeks on the government's "amicus" or friend of the court" brief, expected to be released this week.

The case involves a white applicant who claims that he was illegally passed over for admission to the University of California at Davis Medical School even though his test scores were higher than some minority applicants who were accepted. The case is to be heard by the Supreme Court in several weeks.

In contributing to a brief on "reverse discrimination," Days, who until this January worked for the NAACP's Legal and Education Defense Fund in New York, now finds himself on the opposite side of the table from old colleagues.

A first government brief maintained that Bakke had a case against the university, though still supporting affirmative action programs. Subsequent revisions are said to strongly support affirmative action programs while walking a tightrope on the distinction between racial quotas and "goals".

"Frankly," says one civil rights attorney, "a lot of people were surprised by the government's first brief. Even though the Solicitor General's office is charged with the responsibility for the case, Days' office had input. And given Drew's record as a civil rights attorney one would be led to believe that the government would support the university."

Days has declined to comment on his role in the Bakke brief.

Born in Tampa, Fla., and raised in New Rochelle, N.J. Days is old enough to remember when a blatant discrimination was for blacks a fact of life. He says he hopes to interject into his new job "a difference in tone . . . to get America to where it sees subtle forms of segregation, to stop trading to the last on code-words."

Unlike many of President Carter's appointees, Days did not work in the Carter campaign and says he was surprised when he got a call late last December to "come to Atlanta to talk to Judge Bell (now Attorney General Griffin Bell)." Days had argued school desegregation cases before Bell, but felt the summons was merely "an honest attempt to consider some black lawyers who wouldn't figure in the final shakedown, so I didn't take it seriously."

Nonetheless, when Bell hesitated about offering Days the post because he didn't want to do something Days might feel was disparaging. Days told him not to agonize over it. He wanted the post.

In many ways, Days is part of that first generation of blacks who have reaped the harvest of earlier civil rights efforts. As a boy, he remembers chatting with Mary McLeod Bethune, the women's and civil rights activist of the Roosevelt era, because she was on the board of the insurance company that his father worked for. His mother is a retired schoolteacher.

"I don't remember anything specific she ever told me," recalls Days. "But I remember that she talked to me like intelligent, thoughtful people talk with small children."

Days' family moved to New Rochelle, N.Y., when he was in junior high school, and he remembers being surprised that the grade schools there were segregated like the schools of the South.

Though Days initially thought of becoming a doctor, he discovered that he did not have much science ability.

By the time he went to Hamilton College in Clinton, N.Y., he'd become more radical and politically active, so that the Law became his goal, he said. At Yale Law School, Days' studies put emphasis on constitutional law, civil liberties and race relations.

During law school, he found himself one of five blacks in a class of nearly 200.

"It was a strange atmosphere," says Days, who though his family wasn't poor, for the first time was among some who were the truly rich. "There is an economic reality at work in law school that some people don't realize. Yale, like other law schools, is committed to the status quo, and there were students there whose fathers and grandfathers were lawyers. They breathed the law, knew what the stock market was all about. All these things were very strange and foreign to me."

The gulf between his background and some of his fellow students came through during his first contracts exam. "A question did not turn on whether the contract was signed, but I answered it that way because I didn't recognize the short-hand signature for signed. The professor just assumed everyone was familiar with it, though it had never been part of the course.He must have gotten a real laugh out of my answer."

To rest from the rigors of law school, Days got involved in the Yale Russian Chorus, a group that sings Slavic songs.

It was through his singing that Days met his wife, Ann Ramsay Langdon. She was a student at Connecticut College where she was studying Russian. The Russian chorus conductor, who was her Russian teacher, needed some female voices and invited her to join.

Ann Days, who is a direct descandant of Sarah Ball, George Washington's cousin is named after the wife of Alexandria's first mayor. The couple has two children, Alison Langdon, 5, and Elizabeth Jamerson, 1.

Ann Days, who is an artist, says that when she first met her husband she "thought he was nice but I wasn't really interested. But he kept writing these really fantastic letters and that got me interested."

Scheduled to go into the Peace Corps in Honduras, she received a final letter from him warning her not to expect him to be around when she got back. So they got married and went to Central America together.

"My mother's reaction was that I was limiting my life," recalls Ann Days. "But Drew told her, and rightly so, that I was doing just the opposite.

"Now I think he's her favorite son-in-law," she says. Though there's been no dissension in either family because of the marriage, Ann Days says their one source of conflict is Days' heavy work schedule.

"If you really dig motherhood and like being a single parent, it's fine if your husband is in government. But I don't like it, and it's something I make quite clear to Drew. So there have been times when he's been stuck taking care of the kids."

Ann Days says that belonging to two women's groups has helped her developed her own personality. "It's difficult to have a separate life when your husband's in government because it's not separate enough by its very native. And I used to feel guilty because I wasn't an assertive as he was and didn't approach people the way he did. But I'm beginning to like the peaceful, alone times I can spend with my art. And I like the loving caring passive side of myself more."

Though she says that her husband is "very conservative, not implusive" and "he doesn't do things that would be frowned on by the mainstream." Ann Days says Days has a lighter side to his personality.

"He does things like sing Renaissance madrigals in the shower and he tells corny jokes. He always said he married me because I'm the only one to laugh at his jokes."

"Drew is a great mix of the legal and humane," says friend Patrick Swygert, a teacher at Temple University Law School, where Days taught as associate professor for two years when he lived in New York.

"Even befor he was appointed and nobody knew he was going to work in the administration, the students at the law school invited him to be their graduation speaker. I think that says a lot about his appeal."