The State Children’s Health Insurance Program expires on September 30, potentially leaving 5 million children uninsured, 637,000 of them in New York State. SCHIP, pronounced ess-chip, originally was signed into law in 1997 as an addition to Medicaid.

Politicians find it hard to end any government program, though, especially one delivering services to children, so reauthorizing SCHIP should be easy. But it isn’t.

That’s because the reauthorization of SCHIP has sparked a philosophical debate over the government’s role in health care. This bill is but one battle in a long ideological war that will not end with the resolution of this legislation. President Bush is prepared to reauthorize SCHIP when Congress returns in September, but he opposes Democratic proposals to expand eligibility to families who are more than 200% above the poverty line. He wants to treat federal-state health insurance like the government treats food and housing — available to low-income Americans who need it, but not to everyone.

By contrast, many congressional Democrats believe that health insurance should be treated like street lighting — available to everyone, and paid for by the taxpayers, as in Europe and Canada. Some Democrats would expand SCHIP to families who cannot be defined as low-income by any stretch of the imagination.

Which side will blink first when Congress reconvenes?

Mr. Bush wants to increase SCHIP’s funding by $5 billion over five years. Only in Congress is this regarded as an insignificant amount. Senate Democrats, led by Montana’s Max Baucus, have passed a bill by a margin of 68 to 31 to increase funding by $35 billion. The House Democrats’ bill, sponsored by Michigan’s John Dingell, the savvy senior Democrat, passed 225 to 204 and goes for broke at $50 billion.

The “compromise” from a House-Senate conference seems certain to exceed Mr. Bush’s declared limits. Will he veto it? Can Democrats muster the two-thirds majorities in each House needed to override a veto?

If a veto comes and stands, the Democratic leadership will have to consider a second-round, and more modest bill. It may try to set up Mr. Bush as hostile to more generous health care for children, but it cannot walk away from the issue altogether.

The number of children covered by government health care programs has been rising. Last year SCHIP covered 7 million low-income children and Medicaid covered 29 million low-income children, 48% of all children, compared with 28% in 1998.

Even so, there are still children without health insurance, and that’s why congressional Democrats want to expand the program. The exact number is uncertain. The administration estimates that 2 million children are uninsured for a year or more. The Congressional Budget Office estimates that 5 million children lack insurance for part of a year.

Many parents don’t register children for SCHIP because they don’t see any reason to do so. Kids are basically healthy, and parents may have to take unpaid time off from work to register them.

If a child gets sick, however, and visits a doctor or an emergency room, the child is usually signed up for SCHIP or Medicaid on the spot. Hence, numbers of children listed as “uninsured” overstate numbers with no care.

To insure more children under SCHIP, Democrats would raise income eligibility well into the middle class. The present limit of 200% of the poverty line is $40,444 for a family of four, although individual states can and do fund higher levels. The Senate would raise the limit to 300%, or $61,000, and the House sets no limit on what states can do. Hence, states such as New York, who are applying to raise the limit to 400% of poverty, or $82,000, would be able to do so.

Mr. Dingell, whose bill, according to CBO, would insure another 5 million children, proposes changes that would enlarge the role of government and diminish individual responsibility and choices within private markets. Here is the philosophical conflict that makes compromise difficult: Mr. Dingell would eliminate co-payments to Medicaid recipients and reduce premiums paid to Medicare Advantage plans, the competitive Medicare program favored by Mr. Bush as a door into a truly private system.

As well as getting rid of elements of choice and competition in the government system, the bill expands the eligibility of pregnant women for government-paid care, raises the age of eligible “children” to 25 — that’s not a typo — and allows states to waive the five-year residency requirement for legal immigrants.

To pay for all this, Mr. Dingell proposes cutting government payments to Medicare Advantage plans and raising $26 billion through hikes in cigarette excise taxes, regressive taxes that fall most heavily on lower-income smokers. Another $570 million would come from taxing existing health plans, punishing those who insure themselves.

Mr. Baucus, whose bill would increase enrollment by 4 million, would fund his bill through $35 billion in higher cigarette taxes.

Bob Goldberg, vice president of the Center for Medicine in the Public Interest, declared that “Congress is expanding an entitlement to families who, according to the Census Bureau, currently spend more per household on restaurants than on health care.”

It would be more useful to look seriously at plans to tax employer-paid premiums as income to employees and to give tax benefits to individuals to buy health insurance. Such tax deductions or credits would encourage insurers to broaden the coverage they offer as they compete for new customers.

Mr. Bush wants to give all families a $15,000 standard tax deduction from income and payroll taxes to buy health insurance. And Senator Enzi of Wyoming has proposed “Ten Steps to Transform Health Care,” a bill that would, in addition to the tax deduction, give subsidies to low income people to buy health insurance. Mr. Enzi would also authorize so-called interstate risk pools that would lead to lower premiums for individual buyers.

Putting such a system into place would require Mr. Bush and congressional Republicans to convince Americans that they would do better with a wider choice of health plans than with the temptation of government-provided plans.

Whoever wins the SCHIP battle next month will have the long-term advantage in shaping American health care.

Ms. Furchtgott-Roth, former chief economist at the U.S. Department of Labor, is a senior fellow at the Hudson Institute.