President Carter's proposed Department of Education appeared to be in severe trouble yesterday as opponents on the House Government Operations Committee readied a fat pack of amendments designed to stall a final vote and kill the bill by delay.

Rep. John N. Erienborn (R-III.) said openly tha he wants to hold up committee action as long as possible by offering a multitude of amendments. With enough delay, he said, it might be too late for the leadership to schedule the bill for floor action, "It's a good tactic," he said.

Eirenborn and other conservatives oppose the bill for fear it will lead to total federal domination and control of education at all levels of government. The AFL-CIO and other labor and minority groups also oppose it, on grounds it will fragment their political clout and remove education from a close connection with related social welfare and health programs.

Some of the labor spokesman fear the new department will be dominated by the National Education Association, the arch-rival of the AFL-CIO teacher union.

The House Rules Committee has notified committee chairman that it won't clear bills for floor action unless requests to do so are in by today.

Yesterday, Erienborn together with Leo J. Ryan (D-Calif.) and other opponents offered so many amendments and used so much time dicussing them that the Government Operations Committee was unable to reach a final vote on the proposed department.

Because the big tax bill is now on the floor, Chairman Jack Brooks (D-Tex.) put over further committee action on the education measure until Monday.

The committee made one major change in the bill yesterday, voting 29 to 9 to include in the proposed new department the $912-million-a-year vocational rehabilitation program now in the Department of Health. Education and Welfare. President Carter opposes this charge.

Rep. John Burton (D-Calif.) said disabled adults collect welfare or Social Security disability payments and need social services, and therefore vocational rehabilitation should be kept in HEW, which administers these other programs too. But the committee voted for the shift anyhow.