THE CARE of children is a family responsibility, but what is the role of government when the family is weak or fails -- and who decides when that moment occurs? These are no idle questions in a world of crack and boarder babies and family's dissolution; U.S. foster care rolls rose 25 percent from 1986 to 1989, the last year for which a good national estimate is available.

Now the congressional Democrats are rightly proposing to put these difficult issues near the top of their domestic agenda. Senate Majority Leader George Mitchell has made a child welfare-foster care bill S. 4 in this Congress, the low number being the badge of high party priority. A similar "Family Preservation Act" is being pushed in the House by a group including Rep. Tom Downey, acting chairman of the Ways and Means subcommittee from which such legislation must emerge.

It used to be said -- in some quarters still is -- that the federal government had no particular policy toward families and children, which some lamented and others, fearing a clumsy federal presence in a personal relationship, regarded with good cheer. But in recent years, two conservative presidents and Democratic Congresses have combined to enact a series of important family and children's initiatives. In part this is a reflection of need -- children are now the poorest Americans -- and in part it has become a matter of vocabulary. The family has become the bipartisan meeting ground of politics. The key to passing almost any important social legislation is to say that families and children, as distinct from such a group as the poor or blacks or city-dwellers, will be the beneficiaries.

The last Congress expanded a negative income tax the government maintains for low-income working families with children, expanded Medicaid so that by about the turn of the century it will serve all poor children under age 18 (it serves only about half now) and instituted a new child-care program. The Congress before adopted welfare reform.

The new legislation is less grand, but would help to round out this agenda. The most important provisions in both the House and Senate versions would give the states more matching money, in the form of an entitlement not subject to the vagaries of the appropriations process, to increase so-called preventive services as an alternative to foster care -- earlier intervention to keep families at risk from breaking up. Congress last tried to lure and shove the states in this direction in 1980, when foster care roles were also rising and it was thought that the pattern of federal reimbursement -- more to finance foster care than to avert it -- was among the reasons.

The new effort won't solve the problems of family break-up and child abandonment anymore than did the old, but it seems calculated to help. As now envisioned, it will not be that costly, and Sen. Mitchell assured potential critics that under the terms of last year's budget agreement the cost would somehow be offset and the bill properly financed.

This is modest but useful legislation, some version of which deserves to be passed.