President Carter's proposed Department of Education neared Senate approval last night after weeks of intermittent debate.

However, final voting on a packet of amendments and on the bill was put off until Monday.

The bill would shift most of the education programs from the Department of Health, Education and Welfare to a new, Cabinet-level Department of Education that would include the overseas schools for children of military personnel, college housing loans and a variety of small programs from different agencies.

The department would have a budget of about $14.3 billion a year and staff that, under an amendment by Sen. Henry Bellmon (R-Okla.), couldn't exceed 17, 239 in its first year.

President Carter proposed the department on grounds it would give education a stronger voice in the Cabinet and more efficient management not burdened by layers of HEW personnel. The proposal is backed by the National Education Association, National School Boards Association, United Auto Workers, American Federation of State, County and Municipal Employees, National Urban League, and a host of education groups.

However, a coalition of conservatives, higher education organizations and some labor groups including the AFL-CIO and the American Federation of Teachers has opposed it and will strive to kill the bill when it comes up for a vote in the House Government Operations Committee, where the matter is considered close.

The argue that a separate department would cause federal domination of educational policy at the state and local level and in the universities or that it would weaken the existing civil rights coalition. Many also believe that the American Federation of Teachers fears its rival, the National Education Association, would dominate the new department.

Sen. Harrison H. Schmitt (R-N.M.), voicing fears of federal domination, said yesterday that "while the federal government provides only 8 percent of the funding, federal control" of education is already substantial and would only increase if major programs were united in a single department.

Sen. Daniel Patrick Moynihan (D-N.Y.) said the real motive for creating the department is a "backroom deal born out of squalid politics" but without amplifying. Listeners took him to mean that the administration is pushing the bill in return for NEA support in the next election.

The bill's floor manager, Abraham A. Ribicoff (D-Conn.), said creation of the new department would improve the qualify of education and end bureaucratic snafus in programs.

The new department would not include some major programs in other departments - veterans' education programs, Labor Department employment training, school nutrition, Head Start. The White House left them out either on grounds they weren't appropriate or for fear that their inclusion would cause defeat of the bill by inflaming some of the client groups.

Last year the Senate approved virtually the same bill 72 to 11, and the House Government Operations Committee passed it 27 to 15, but it never reached the House floor and died.

This year there is a new composition in the House committee and the vote is considered tight there.

Before the Easter recess, the Senate tacked an amendment permitting public school prayer onto the bill by 47 to 37, but it was later stripped off in a 53 to 40 retally. Its inclusion would have killed the bill because of the controversial nature of the prayer issue.