THE HOUSE Banking Committee has reported out its annual housing bill, continuing one of the longest-running budget and policy fights of the Reagan administration. This is the fight over subsidized housing for the poor. In the early 1970s the low-income housing programs were a relatively minor budget item. They have snowballed into the third-largest federal welfare program, after Medicaid and food stamps. They will cost perhaps $12 billion in the next fiscal year.

In a way, these housing costs snuck up on the government. Congress fell into the habit, through administrations of both parties in the 1970s, of adding several hundred thousand units of subsidized housing every year. The annual increments seemed small, but their cumulative effect was large, because each unit involved a lasting federal commitment. The government promised landlords who built or modernized units for the program that it would supply them with subsidized tenants for up to 20 years.

By the end of the 1970s some $200 billion in such obligations had built up -- and even so there are enough subsidized units for only about a fourth of the households theoretically eligible. The Reagan administration came to office determined at least to stabilize, if not reduce, these costs. It asked Congress to freeze the number of units in the programs, rescind unused appropriations, raise the tenant share of rents from 25 to 30 percent of income (the government pays the rest) and consider a shift to vouchers, which would allow much greater flexibility in setting future spending levels.

The housing programs have never been as important politically as Medicaid, food stamps and Aid to Families with Dependent Children. The House committee and to some extent its Senate counterpart have nevertheless worked to keep the programs whole. In 1983 the House committee went so far as to make administration acquiesence in a housing bill the price for continuing U.S. participation in the International Monetary Fund. The administration has been successful in cutting the growth of the programs and shifting the mix to less costly kinds of housing. But the new bill, ignoring an administration call for a freeze, would nevertheless authorize 100,000 more units next year, the same as this year.

In this as in many other areas, what the administration has done is blunt past policy but not replace it. Programs continue, but in less generous and costly form. Policy is a hybrid. Given the competing pressures to cut the deficit and sustain the poor, that may not be a bad result.