AN EIGHTH of the U.S. population lacks health insurance. Many of these uninsured have marginal incomes, and providing them with the coverage that they must now either beg or do without is as great a health care problem as the country faces.

In the 1988 campaign, Democrats urged as a partial solution that all but the smallest businesses be required either to provide or to pay taxes toward health insurance for the families of all employees. George Bush rejected this mandated benefit, suggesting instead that he would favor expanding Medicaid, including by letting the needier uninsured buy into the program, their premiums scaled to ability to pay. That suggestion was vague, however, and never developed; after the campaign the idea was dropped.

But not by everyone. In the back of this year's budget agreement between the president and Congress is about $40 million to be spent in the next several years on demonstration projects in the states to test the extension of Medicaid on contributory and other bases to the near-poor uninsured. Its principal sponsors were Sens. George Mitchell (D-Maine) and John Chafee (R-R.I.), both of whose states might be testing grounds.

The demonstrations, if they go forward, will join a series of recent efforts to narrow the gap between public and private insurance by raising the income levels at which public insurance is available while lowering those at which private insurance can be had. Among many other steps, these involve breaking the mold on Medicaid, which for years has been much more a program for welfare families than the health insurance for all the poor that its supporters touted.

Medicaid now covers fewer than half the poor, but in recent years Congress has steadily expanded its scope. The law does not yet require that it cover all the poor but does envision that over time, it will cover all poor children. In the meantime, the welfare reform act of two years ago extended the time a welfare family could remain on Medicaid if the mother went to work and provided that the family could continue on a contributory basis even after that. The demonstration projects would support similar extensions of the program to households with incomes up to 150 percent of the poverty line. There are also several situations now in which states either can or must use Medicaid funds to pay private insurance premiums -- at an eligible person's place of employment, for example -- when that is cheaper than enrolling the person in Medicaid directly. The budget agreement also provides new tax credits to help the working poor with children pay such premiums, and Medicaid is now used to pay the premiums and other costs of the elderly poor in Medicare.

None of these steps is millennial, but all are headed in the direction of creating a web of public and private coverage based on income in which the government one way or another contributes the share of cost that a family can't. The problem is anything but solved, but in these small ways the government has begun to chip away at it.