The steam seems to have gone out of the push for educational vouchers, and that probably is a good thing. But the heat is building for a major push for tuition tax credits, and that is probably bad: bad at least for the future of public education.

I won't go so far as to suggest that passage of a tuition-tax-credit bill would necessarily sound the death knell for public education. But there can be little doubt that it would weaken the public schools, which are weak enough already.

The idea of the several proposals is that parents whose children attend non-public schools would be able to deduct a part of the tuition cost -- $250 under the bill introduced by Sen. Moynihan (D.N.Y.) -- from the amount of federal taxes they owe.

The notion has a lot of things going for it. Equity, for one. Parents of children in private or parochial schools are paying twice for their children's education: once in their taxes, which support public schools, and once in their private-school tuition. To the extent that their decision to enroll their children in non-public schools relieves the public schools of a part of their burden, it seems fair that the parents should get part of their money back. (The same argument could be made, of course, for childless taxpayers, who, similarly, help to support schools from which they derive no direct benefit).

But the broader policy question has to do with the nature and support of public education. And here it is important not to be misled by the $250 figure of a specific proposal. Clearly, not many families would make their decision for private or public education primarily on the basis of a $250 tax credit. Only for poor families would $250 be that significant, and the poorest families are precisely those for whom a tax credit would mean least, since they tend to pay very little federal tax to begin with.

But the $250 is the camel's nose under the tent. Once the principle is established in favor or public subsidies for private education, the recurring battles will be over the amount of the subsidy, with the probably goal being either an amount equal to the actual cost of the private-school tuition or, alternatively, the per-pupil cost of public education.

Here you are talking real money -- and a real threat to the public schools.

The most appealing argument in behalf of tuition tax credits is that it would give to middle- and lower-income parents the same choices already available to the wealthy.

That many parents consider the choice important is evident in the number of children already attending non-public schools -- including children of parents who stretch their modest incomes to get them into parochial or private schools.

Nor is there any mystery as to why they make the sacrifice. Catholic schools, even in the big-city slums, routinely outperform their public-school counterparts in terms of pupil performance.

But who will contend that that superior performance is wholly, or even primarily, the result of the superior teaching methods of the parochial schools? Clearly at least a major part of the difference is that the private and parochial schools don't have to be bothered with disruptive children, or truant children, or children whose parents are unconcerned about their education.

Given those advantages, wouldn't most of the public schools do a good deal better? And without those advantages, wouldn't most of the private schools be a good deal worse? Surely it wouldn't cure what ails the public schools simply to replace the harried public school teacher with the nearest available teaching nun.

What we are talking about is the flip side of the "choice" on which the tuition tax credits are premised: the selectivity of the non-public schools. It doesn't matter that much whether the selectivity results from screening at the admissions office or from self-selection by the parents.

But shouldn't parents have the right to choose? Of course. The real question, though, is whether the government ought to subsidize that choice.

The cities are still paying for the government-subsidized power exodus of middle-class families to the suburbs. We ought to think long and hard before we encourage and subsidize a middle-class abandonment of the public schools.