The House late last night beat down a move to kill President Carter's proposed department of education.

The 266-to-146 rejection of the proposal by Rep. David Obey (D-Wis.) to kill the bill came after a plea by House Speaker Thomas P. (Tip) O'Neill Jr. to save the measure.

"Are we being fair to the president of the United States who has sent this question up?" he said to the House before the vote. "Don't let the bill go down this way."

After the vote the House adjourned for the evening.

Obey told the House that the only reason it has been able to override vetoes of big money bills for labor, health, education and welfare programs was by forging a coalition "composed of labor, composed of eduction, composed of all the health lobbies." Creating a separate department of education has split up the coalition, Obey said.

The House vote came after three days of bitter debate and attempts by conservative opponents to stall the final vote on the bill in the hope of gaining more support.

Vice President Mondale has been active in trying to hold troops in line, with appeals to Democrats to continue support and to several civil rights organizations which were dismayed by some amendments added by Walker and his allies.

The bill, strongly pushed by President Carter as giving education more visibility and clout through creation of a seperate Cabinet-level department, unites a number of major programs from health, education and welfare and other agencies into a $14-billion-a-year, 18,000-employe unit.

It is backed by the National Education Association and numerous other education organizations but opposed by the American Federation of Teachers, AFL-CIO and some back and civil rights organizations on grounds. It could weaken existing lobbying coalitions. Some conservatives also oppose it for fear it would dominate local educational agencies and destroy independent policymaking.

In three days of voting, Walker, John N. Erlenborn (R-Ill.) and other opponents made little change in the basic structure of the bill. The only major structural changes killed the transfer to the new department of American Indian schools and certain health training programs.

But Walker and others succeeded in adding school prayer and antibusing amendments, plus language barring the new department from ordering quotas, ratios and "other numerical requirements" relating to race, creed or national origin or sex.

The United Auto Workers said yesterday that because of these amendments, it can no longer support the House version of the bill though it still favors creating a new department.

Carter administration spokesmen said they would work to have these provisions dropped in conference with the Senate, whose version of the bill does not contain them. The Senate passed the measure April 30 by a 72-to-21 vote.

The fight over the department of Education has all along been in part a bitter struggle over turf between the National Education Association, the largest professional educator group with about 2 million members, which supports the bill, and the American Federation of Teachers, the NEA's arch-rival, which opposes it.