The cream thickened yesterday in the dairy price support saga. Specifically, the House dairy subcommittee faced a choice between the Reagan administration's plans and the dairy lobby's plans, and went for the lobby's by 7 to 6.

At bottom the issue is how much money milk consumers and taxpayers pay milk producers. But as usual in this town, the fight is being conducted in arcane terms -- almost a foreign language.

The Reagan administration, eager to win a first symbolic vote on budget cutting, has proposed a bill to skip a scheduled April 1 increase in the price the government will pay for surplus milk products. This would save the treasury about $147 million, and save many millions more for consumers who will have to pay higher milk prices if the support price is raised.

This is the first step in what will eventually be more elaborate administration efforts to reduce the dairy program, which could easily cost the tax-payers $2 billion this year. Its costs have been shooting up recently because expanding production -- encouraged by a relatively high support price -- has far exceeded demand.

The dairy lobby is one of the best financed, most effective and most generous (in terms of campaign contributions) of any in Washington. Its principal Washington operator, Patrick B. Healy of the National Milk Producers Federation, has a sensitive finger when it comes to feeling the prevailing winds. Healy decided months ago that the milk producers ought to propose a new formula for dairy price supports that would cost the government less than the current one.

Healy and his staff formulated a price support plan, and they have been circulating it on Capitol Hill for weeks. They also have been discussing it with Reagan administration officials in the Department of Agriculture. Essentially, the plan calls for a sliding price support that would rise when government stocks of surplus milk products are falling, but hold steady when surpluses grow.

Yesterday, Rep. Thomas R. Harkin (D-Iowa) and others on the House dairy subcommittee introduced what amounted to Healy's new proposal. They introduced it as a substitute for the Reagan administration's one-sentence bill to skip the scheduled April 1 increase in dairy price supports. And the subcommittee endorsed the idea.

Loyal Republicans on the panel tried to insist on the Reagan administraion's simpler approach, but they were beaten by one vote. Two of the votes cast against the Reagan plan came from Republicans: Steve Gunderson (Wis.) and James M. Jeffords (Vt.), both from areas heavily populated by dairy farmers.

If the subcommittee's action were to prevail in the House and then the Senate, the Reagan administration would suffer a humiliating defeat on the first congressional action on its budget-cutting crusade. But the odds against this happening are enormous.More likely, the administration will have its way -- as even the dairy industry's lobbyists realize.

So why the fuss?

Because in Washington illusions can be as influential as realities. The dairy lobby realizes that it is the first special interest to go up against "the great communicator, who has really got the country snowed," as one dairy lobbyist described the budget-cutting crusader who is now president of the United States. The industry wants to make an impression of maximum possible strength, not to retain the April 1 price increase, but to maximize the benefits offered to dairy farmers in the comprehensive farm bill that Congress will enact later this year. The appearance of legislative influence now should have a positive benefit later, or so the dairy industry hopes.