PRESIDENT REAGAN'S tax cut has now passed through the first phase of congressional examination. The administration has laid out a detailed plan, and it has gone through the first round of hearings in the House. The crucial development in this early is that the president's supply-side theory seems to have made no coverts.

A lot of people favor a tax cut, but only on the conventional grounds that inflation automatically imposes increases that have to be offset by Congress from time to time -- and the time is now due. Except for the committed few theologians of the movement, it is hard to find much enthusiasm for the specific logic of the supply-side tax cut. The truly interesting thing is the cool and distant reception it has got in the financial and business world. The people in the money markets remain unsentimental and agnostic. They keep looking out -- to judge from the flood of speeches, newsletters and analysis -- cannot for the life of them see Mr. Reagan's vision of booming prosperity admist steadily sinking inflation. Instead, they see larger deficits than Mr. Reagan does, resulting in unpredictable interest rates and poor economic growth.

The supply-siders' failure to hold the initiative has substantial political importance. It means that Congress will have a free hand to take the president's plan apart and put it back together along lines that seem more promosing. Since that's not a rapid process, it also means that the bill will move on a much slower schedule than the administration expects.

The supply-side theory is in serious trouble at several points. It argues that lower marginal tax rates are essential to provide incentives to work harder and save. Yet for the vast majority of taxpayers the Reagan plan offers no chance at all in marginal rates. Inflation will keep pushing them up through the brackets as fast as the rates in each bracket are reduced. Congress, sensibly enough, is thinking about writing in explicit inducements for saving and investment.

There's a lot of resitance in Congress to Mr. Reagan's idea of legislating a series of tax cuts several years into the future. No doubt some congressmen fear an attempt to force them into further spending cuts, still unspecified, in the years ahead.But a lot of people in both parties, not being new to Washington, think that it will work the other way -- that the present enthusiasm for budget-cutting will diminish as the next presidential election gets closer. That would leave tax rates declining without any balancing reductions in spending -- resulting, once again, in big pre-election deficits.

The argument for three years of tax cuts in one bill is that it would let people know what to count on. But taxpayers know that their personal taxes in 1984 will be influenced as much by future inflation as by present legislation. That's the point at which the supply-side logic goes circular. If people don't believe that inflation will be falling rapidly by 1983, the plan won't work. And if the plan doesn't work, inflation won't be falling in 1983.