PRESIDENT REAGAN'S struggle with the rebellious Republican congressmen is the more dramatic side of the campaign to enact the tax bill. But it's important not to let that quarrel obscure a clear view of this bill, and why it's necessary. In his television address last night, Mr. Reagan made the right case for it.

The original Reagan tax program hasn't worked, despite the author's claims to the contrary. Last year's enormous tax cuts were supposed to set off a great boom in investment and production that would send revenue soaring. As it's working out, the tax cuts have left the government with very large budget deficits that, in turn, keep interest rates intolerably high. The present bill is designed to be large enough to make a difference in deficits and interest levels, without being large enough to choke off an economic recovery over the coming year. People who oppose this tax bill have to answer a question about interest: how else are the rates to be pulled down?

In conventional terms, it's not good policy to raise taxes in a recession -- but this bill is not a conventional tax increase. Last summer's legislation contained a long series of tax cuts to be phased in over five years. The present bill before Congress -- as Mr. Reagan correctly emphasized -- would cancel, or offset, only about one-fourth of the reductions, present and future, in the 1981 legislation. The net effect is still a large cut.

The bill's chief purpose is to raise some money to pay for things -- like national defense -- that the country needs. But it would also make a major contribution to the basic fairness of the tax system. For example, in its haste last summer, Congress passed depreciation provisions that, for some industries, actually create subsidies for investment. The depreciation allowances, together with other tax benefits, turn out to give the investor more than the full value of the investment. That's wrong in principle and, worse, it discriminates in a haphazard pattern against certain industries. This year's bill would repeal the subsidy.

As for personal taxes, a system like this country's -- in which nearly 100 million people file returns every year -- must depend chiefly on voluntary compliance and good faith. When honest taxpayers see evasion around them, and when they see the government do nothing about it, the whole base of the system is eroded. People who work for weekly wages know that taxes are deducted from their checks. Why shouldn't people who get interest and dividends be subjected to the same discipline -- particularly when the failure to report this income is widespread and notorious? Tips are another kind of income in which evasion is conspicuous. If Congress endlessly tolerates billions of dollars' worth of cheating in these areas, how are other taxpayers to feel about their own obligations?

Both the administration and Congress have now combed intensely through the entire federal budget several times in the past 18 months, and both seem to be having difficulty finding much more to cut. They are now getting down to the levels of spending that most Americans seem to consider irreducible. The easy targets are gone. Public support for more free-swinging chops is vanishing. That leaves only one way to begin closing that gaping deficit. Congress and Mr. Reagan now need to reinstate at least a small part of the revenue that, last summer, they prematurely gave away.