President Carter asked Congress yesterday to create a Cabinet-level department of education with control of 164 educational programs now scattered throughout the government, a budget of $17.5 billion a year and a staff of 23,325.

The new department would include most of the education programs in the Department of Health, Education and Welfare ($12.9 billion). Head Start ($680 million), the Agriculture Department's child-nutrition education programs ($2.985 billion), overseas Defense Department schools ($350 million) and Bureau of Indian Affairs schools ($271 million).

It would also take over from HEW supervision of Howard University, Galludet College, the American Printing House for the Blind and the National Institute for the Deaf.

However, the giant $2.6 billion-a-year veterans' educational programs would remain in the Veterans' Administration. Both the American Legion and the Veterans of Foreign Wars had made plain they would go all-out to defeat any plan removing the veterans' schooling programs from VA, which they say understands their problems better than anyone else.

The reorganization proposal also didn't include the National Foundation for the Arts and Humanities, most of the National Science Foundation (NSF), certain juvenile delinquency programs in the Justice Department, public broadcasting, substantial health training programs, the Smithsonian Institution, the vocational rehabilitation programs or the job-training programs of the Labor Department.

Although the final proposal avoided antagonizing the immensely powerful veterans' bloc, it will not have clear sailing, even though it was warmly applauded by Sen. Abraham A. Ribicoff (D-Conn.), a former HEW secretary and now chairman of the Senate Governmental Operations Committee.

Ribicoff said fears of some community groups that it may weaken their hold on Head Start, fears of some Indian groups of the transfer of Indian education form Interior, and objections by some transfer of child-feeling out of the Agriculture Department would have to be considered.

Marian Wright Edelman, director of the Children's Defense Fund, said that proposing to include Head Start "is a betrayal of poor and minority children throughout the country" because it shifts them from an agency where they receive comprehensive services including health, nutrition and social needs to one which will be dominated by narrow established educational interests. "This is a program which is working in its present form with a large parental and community action component."

She said key black leaders, including Vernon Jordan of the National Urban League, Coretta King, Carl Holman of the Urban Coalition, the Rev. Jesse Jackson and Bayard Rustin told the president recently not include Head Start.

Others believe some Cabinet officers losing big programs to the new department might covertly fight to hold their "turf."

Office of Management and Budget Director James McIntyre, who outlined the plan at a hearing before Ribicoff's committee, said creation of a separate education department would remove education from "second-rate status" and give it a Cabinet voice of its own.

A spokesman for the National Education Association called the plan a "significant move," and said he hopes for rapid congressional action.Many in the education field say they believe separate Cabinet status would mean more federal dollars for schools.

However, the American Federation of Teachers said the AFL-CIO opposes it and "we don't like it. We're still against a separate department of education. We think it would detract from the central need of increased financial support by breaking the alliance between labor, welfare and education forces, and it would isolate education from other human resource activities of the government such as welfare and day-care."

Sources said the president, in a series of decisions late Thursday and early yesterday, had opted for a bigger department than his advisers had expected at this time. Initially, they said, it didn't appear that child-nutrition, Indian schools, overseas DOD schools and Head Start would be included in part for fear it would invite opposition from "client" groups confortable where they are. But the president decided to include them.

McIntyre, explaining why the GI Bill veterans' education programs were left in VA, said, "The president said he was committed to one-stop shopping for veterans."

In terms of money, the Cabinet agency that will lose the most if the proposed reorganization goes through is HEW. Secretary Joseph A. Califano Jr.'s department would lose not only $12.9 billion in basic education programs, but also the $680 million Head Start program and nearly $100 million additionally from other programs.

Losses by HEW make up over three quarters of the budget of the new agency. Moreover, most of this money is discretionary funds, where the HEW secretory can have some say in helping shape programs.

Of the total $180 billion estimated 1979 HEW outlays, nearly $162 billion consists mainly of Social Security and Medicare payments for which HEW acts basically as a transfer agent to shift money from the taxpayer to the aged and the ill, with little policy control. Nevertheless, HEW said Califano "will of course support the president."

Of the new department's personnel, about 5,000 would come from HEW, 6,500 from the Interior Department Indian Schools Division and 10,000 from the Defense Department's overseas schools.

Among smaller programs included in the plan: college housing, certain science education programs from NSF ($56 million), HEW civil rights enforcement for education ($50 million), HEW's Telecommunication Demonstration Program and some HEW health professional and nursing training loan programs ($30 million).