President Reagan, who enjoys purveying sunshine, ought to have a wonderful time traveling around the country selling his new tax plan. True, there are a few clouds on the horizon: "the privileged few" stand to lose some tax breaks. But the proposal cuts taxes for everyone else: "You bet it will," the president said. "We call it America's tax plan."

This sort of upbeat message is, the president's aides note, more to his liking than the spread-the-pain pleading needed to sell his budget plan. No doubt he will continue trying to keep the two initiatives -- budget cuts and tax overhaul -- separate in people's minds. Still, it will be hard to hide the unfortunate relationship between the two.

The federal budget deficit, after all, is nothing more or less than what you get when you subtract revenues from spending. If popular programs need to be cut in order to start reducing an already monstrous deficit, the problem will only get worse if taxes are cut again.

The administration is doing its best to make its proposal look "revenue neutral" -- what they call a plan that produces roughly the same tax flow as current law. But the Treasury's own costing shows the plan losing $7.3 billion in revenue in 1988, Congress' target year for getting serious about the deficit. That loss would be very hard to offset by further reductions in the same domestic programs already targeted for new big cuts.

Moreover, keeping the red ink from rising above $7.3 billion requires some heroic assumptions. One is that, thanks to the supply-side response to the new cuts in tax rates, the economy will grow faster than the relatively robust rates already assumed by administration forecasts. Another hard-to-believe premise is that Congress will go along with a plan to extract almost $60 billion in "transitional" taxes from the same corporations that will be hardest hit by the proposed rollback of the corporate tax benefits enacted in 1981. Or that Congress will agree to phase out some deductions before phasing in rate cuts in order to make the initial tax loss smaller.

Still less likely is that Congress won't be pressured into relenting on some other proposed reforms or, as has always been the case with other tax bills, into adding new tax goodies. It won't take much of that sort of compromising before the program ends up making the income tax code not only more cumbersome and unfair than it already is, but also a great deal less lucrative for the Treasury.

The tax reform plan, remember, offers substantial and hence costly new breaks for taxpayers. The cuts in income and capital gains tax rates, most valuable to top-bracket families, will cost the Treasury more than $65 billion in 1988. The near doubling of the personal exemption, of greatest value to large well-off families, will cost more than $40 billion.

In comparison, the big revenue gainers are few. The plan would make many needed reforms such as limiting (at least a little) deductions for expensive business meals, prohibiting deductions of country club dues and making real estate and other shelters less attractive. But the returns from these reforms are more moral than financial.

Apart from the special "transitional" tax, there are only two large expected increases in revenue. One is the repeal of the investment tax credit, sure to be strongly opposed by many businesses. The other is to no longer allow deduction of state and local taxes, an expense the administration categorizes, curiously, as a "preferred use of income." Apart from how hard it is to imagine that anyone prefers using his money for state and local taxes, that change is vulnerable on the general principle that you ought not to tax a dollar that has already been taxed away.

Some other features would be bad policy. What possible justice can lie in making people with small fringe benefits pay taxes on all of them while people with generous benefits go largely untaxed? Or in transforming the child care credit into a deduction so that it has greater value for families who can better afford to pay for their own child care? Or raising taxes on two-worker families while providing new investment tax benefits for non-employed spouses in well- off families? Or limiting interest deductions except for people with large investment income?

Few people may be troubled by these quibbles. Even fewer are likely to worry, at least for the moment, about how to fill the larger revenue gap the plan is likely to create. Many people may well sit down and, as House Ways and Means Committee Chairman Dan Rostenkowski urged, write "Dear Rosty" letters demanding that Congress face down the special interests and give them the tax breaks the president wants. That will leave Congress, which still hasn't figured out how to pay for the 1981 tax extravaganza in which it happily participated, struggling to figure out how to make good on the president's new promises.