Amid indications that the Reagan administration's choice to head the Equal Employment Opportunity Commission would fail to gain approval of a Senate committee yesterday, the White House had voting on the nomination postponed.

The nomination of William M. Bell, 55, of Detroit, has run into a storm of opposition from women's, black, and Hispanic organizations arguing he is unqualified to run the chief federal agency charged with enforcing laws against employment discrimination. It is one of the first times in memory that black groups have opposed the nomination of a black to a job of this significance.

White House spokesman Larry Speakes said, "The president still stands behind the Bell nomination." The administration requested that a vote by the Senate Labor and Human Resources Committee scheduled yesterday morning be delayed a week, Speakes said, because it realized the nomination was controversial.

Democratic head counters claimed to have enough votes to get an unfavorable recommendation on the nomination in committee and Republican staff members did not disagree. Two committee Republicans, Sens. Lowell P. Weicker Jr. (Conn.) and Dan Quayle (Ind.), announced before the scheduled vote that they would join Democrats in opposing Bell's confirmation.

A spokesman for Quayle said he met Bell this week and found him to be personable but wondered "if there isn't a more qualified person with more experience in the area."

A graduate of the University of Michigan business school, Bell is the president and only employe of his own recruiting firm, Bold Concepts Inc. In response to questions from the Senate committee, Bell said his firm has placed no persons in jobs this year and he has never supervised more than four employes. In an annual report filed with the state of Michigan two years ago, Bell said the total assets of Bold Concepts Inc. were $500. He listed himself as the president, the secretary and the treasurer of the corporation and his wife Patsy as vice president.

If confirmed, Bell would be the first fulltime chairman of the EEOC who was not a lawyer. He acknowledged in an interview last week that he had attended the University of Detroit Law School from 1948 to 1950 but left before graduating. "I really didn't care for it and I wasn't very successful at it and I was called in the Army and I really didn't want to resume when I came out," he said.

Sen. Thomas F. Eagleton (D-Mo.) was the first member of the Labor and Human Resources Committee to declare his opposition to the nomination; in doing so, he urged civil rights leaders to join with him.

"I know this may be a difficult position for many of you to take," Eagleton said in a letter to them, "but it is my strong belief that, after four years under the chairmanship of William Bell, the EEOC will be in such disarray and disrepute that it will take decades to rebuild any effective enforcement of . . . employment discrimination statutes."

Coordination of the civil rights groups' efforts has been lead by Arnoldo S. Torres, executive director of the League of United Latin American Citizens (LULAC). He has been joined by the Urban League, the NAACP, the National Organization for Women and other women's and civil rights organizations.

The White House has tried to counter this opposition with endorsements of Bell from other Hispanic groups such as the National Alliance of Spanish-Speaking People for Equality Inc. and the Hispanic American Cultural Effort. Bell was in Washington earlier this week meeting with them as well as senators and White House aides.

Word has been passed that if Bell is confirmed, he will appoint a Hispanic to be executive director of the EEOC. The name most often mentioned is that of Mike Martinez, a Mexican-American lawyer, from Utah, the home state of Sen. Orrin G. Hatch (R), chairman of the Labor and Human Resources Committee.