Fervid desire to cut the federal budget took hold of the House Agriculture Committee yesterday, giving President Reagan a decisive victory on the milk-price support issue.

The key vote came out 25 to 16 in Reagan's favor -- a far better margin than the White House could have hoped for when committee members assembled after lunch yesterday to consider whether dairy farmers should receive a scheduled April 1 increase in the price support for milk. President Reagan says they should not -- to save the treasury about $140 million, to save the consumers millions more and to try to persuade farmers to produce less milk.

But the margin of victory disguised a tense confrontation between the dairy lobby and its allies and the budget-cutters on the committee loyal to or intimidated by President Reagan. Pro-dairy members devised an ingenious compromise that would have given the dairy lobby a psychological victory while saying the federal treasury perhaps 85 percent of the money Reagan's plan promises to save. For a time, Republicans on the committee loyal to the president thought this maneuver might carry by a one-vote margin, but during the afternoon the tide swept back in the budget-cutters' direction.

Rep. Tom Harkin (D-Iowa), chairman of the committee's dairy subcommittee, obviously realized that he couldn't find enough votes in the committee to support a measure his subcommittee had approved Wednesday, which amounted to extending the existing dairy program at slightly lower price-support levels while saving the treasury as much as $120 million this year.

So yesterday Harkin tried a new approach. When Rep. Paul Findley (R-Ill.) proposed the administration plan to skip the scheduled April 1 price support increase, Harkin suggested an amendment.

Under current law the price support is supposed to be 80 percent of "parity," a figure based on the pre-World War I purchasing power of a gallon of milk. Because inflation steadily pushes this partily level higher, skipping the April 1 adjustment in the price support would mean farmers would get about 73 percent of parity for their milk at the end of this month. The lower figure represents the amount of erosion in purchasing power because of inflation since the latest support price was set last fall.

Harkin's amendment would have guaranteed that the price support could not fall below 75 percent of parity under any circumstances. This would mean that diary farmers would receive a small increase in the price support April 1.

"No president . . . gets 100 percent of what he wants," Harkin pleaded with his colleagues yesterday. By giving the farmer a small increase that might cost the treasury just $20 million this year, Harkin said, "we'll tell those hard-working diary farmers out there . . . that we're not going to just throw them to the wolves."

Several members said approvingly that Harkin's plan would give Reagan "most" of what he wanted, but neither the White House nor its allies on the committee would settle for most. As Rep. George Hanson (R-Idaho) put it, "we can't start right here eroding and whittling on the first" budget-cutting proposal to come before Congress.