Refusing to be cowed by either the Reagan administration or the milk lobby, the House yesterday adopted a middle-ground dairy price support program that the White House says is too generous and dairy groups call not generous enough.

An administration-backed proposal, approved by the Senate last month, was rejected by a vote of 243 to 153 as the House began debate on a bill that will govern federal farm programs for the next four years.

The chamber adopted a compromise by Rep. Berkley W. Bedell (D-Iowa), estimated to cost at least $535 million more over the life of the bill than the Senate version. Bedell's alternative would also scale back other parts of the farm bill in an effort to bring it partway back within the budget.

The administration proposal was put forward yesterday by an unlikely liberal-consumer-conservative coalition led by Reps. Barney Frank (D-Mass.) and Paul Findley (R-Ill.).

After the Frank-Findley amendment was defeated, a dairy-state proposal by Rep. James M. Jeffords (R-Vt.) to lift support prices back to a level that would have cost an estimated $2.9 billion was rejected, 277 to 123.

The debate was predictable and familiar. Dairy-state legislators warned that further curtailment of price supports would be fatal to thousands of small dairy farmers. Administration and consumer allies cautioned that, without major changes, the government would spend billions of dollars for surplus milk products.

Rep. Tom Daschle (D-S.D.), for instance, complained that the House would surrender its independence to the White House if it went along with the Frank-Findley plan. "The White House has played a very heavy role in this ....We didn't write this bill. It was written when the Gramm-Latta budget package was written," he said.

But Frank argued that only his approach contained a "fail-safe" provision that would allow dairy supports to be kept within budgetary controls if government surplus acquisitions began to rise.

Rep. Tom Harkin (D-Iowa) charged that the Frank-Findley amendment was "not an attempt to help consumers.... It is nothing more than an attempt by Mr. David Stockman of the Office of Management and Budget to destroy a dairy program that we have had since 1949."

But Agriculture Committee members pushed hard for the middle-ground approach, apparently on the theory that they must have chips for bargaining with the Senate when the two chambers meet in conference to work out a final version of the farm bill.

The dairy compromise would, like the administration plan, continue price supports at $13.10 per hundredweight during fiscal 1982, but allow increases in subsequent years if Commodity Credit Corp. purchases of excess products are held below certain trigger levels.

Bedell's amendment was part of a package the House overwhelmingly approved on a 400 to 14 rollcall in an attempt to bring the Agriculture Committee's bloated bill back closer to budget limitations.

The Bedell plan, a substitute for the committee bill, still would be some $500 million above the budget.