This week’s battle over expansion of the State Children’s Health Insurance Program, or SCHIP, due to expire on September 30, is a foretaste of the larger campaign that will be under the next president over how Americans will get their health care — through government mandates or programs, or through a broader choice for individuals of private plans. It’s HillaryCare vs. RomneyCare in microcosm.

First, a quick recap of the SCHIP battle. Both Republicans and Democrats want to raise the amount the federal government spends on health care for low-income children.

President Bush wants a $5 billion increase over five years, and the Democrats want a $35 billion raise to expand the program to children from families earning more than the current 200% of the poverty line. The president has promised to veto the larger increase.

On September 25 the House voted 265 to 159 to pass the $35 billion expansion of SCHIP, funded with increases in tobacco taxes, yet fell short of the 290 votes needed to override the promised veto. The Senate yesterday passed its version of the bill by a veto-proof margin.

Having passed a $50 billion increase for SCHIP only in August, the House Democrats reckon that by comparison, a $35 billion bill would retain the Senate majority on the bill and gain Republican House support.

But the $35 billion bill won’t survive a presidential veto and SCHIP is scheduled to expire on September 30. Instead, Congress will temporarily extend SCHIP funding through a “continuing resolution,” which will keep funding at current levels through November 16.

This will give Congress and the president additional weeks to decide whether to bill taxpayers for a $5 billion increase, a $35 billion increase, or something in between.

The crucial question for American health care — for Americans of all ages — in the next few years is similar to the SCHIP issues. Who should be insured under federal government plans, and who under private plans?

All presidential candidates agree that America’s health care system needs change. Not surprisingly, plans from the leading Democratic candidates want to provide insurance either through the federal government or through a government-controlled plan, in which the government determines pricing and coverage of private insurance.

Republican plans focus on expanding private insurance and giving low-income Americans funding to buy it.

Senator Obama’s Plan for a Healthy America would create a new national health plan, open to everyone, modeled after the Federal Employees Health Benefits Program. “The new public plan will include coverage of all essential medical services,” and “participants will be charged fair premiums and minimal co-pays.” People who don’t qualify for Medicaid or SCHIP would receive subsidies for premiums.

In addition, a proposed National Health Insurance Exchange would regulate the private insurance market to “ensure fairness” and make sure that private plans are as generous as the national plan. Employers who don’t offer health insurance would contribute towards the national plan.

Senator Clinton’s American Health Choices Plan also would open the federal employees’ plan to the public. In addition, it would create a new public plan, similar to Medicare.

People would also have the option of keeping their own private plans, which supposedly would be less expensive due to federal regulation of pricing and product — assuming plans wouldn’t disappear altogether. Employers would be required either to cover workers or to contribute to the public plans.

To pay for the expanded federal health system program, Mrs. Clinton would raise $110 billion by, among other means, cutting payments to doctors who care for Medicare patients ($10 billion), regulating prescription drug prices ($4 billion), “modernizing” the health system ($35 billion), and allowing the Bush tax cuts to expire for households earning over $250,000 ($52 billion).

Under both the Clinton and Obama approaches, the excessive regulation of private plans is likely to make them collapse and disappear. Americans would be forced on to the public plans, which would be partly funded by tax revenues and partly by employers.

Such revenue sources would be inadequate to meet the costs of federal health care for all Americans, so health care would likely be rationed instead either by longer waiting times, as is the case in Canada or Britain, or by controls over permitted drugs or procedures. Mr. Obama’s use of the phrase “essential medical services” is particularly revealing.

In contrast to the Democrats, Mitt Romney and Rudy Guiliani encourage the broader development and growth of private health insurance plans. Since they aren’t setting up new public plans, there’s no opportunity for private plans to lose market share.

Mr. Romney wants to bring down the cost of private insurance not by regulation, but by deregulation and competition. State insurance markets would be permitted to offer a broader range of plans, and health insurance premiums and other qualified medical expenses would be tax-deductible.

Health savings accounts would be expanded, and low-income Americans would get federal or state help to buy their own private insurance. Medical malpractice reform would end frivolous lawsuits and cap punitive damages, something that isn’t mentioned by Democratic candidates.

Mr. Giuliani suggests giving all Americans an income tax exclusion of $15,000 to buy private health insurance. Low-income Americans would receive a “Health Insurance Credit” so they could purchase their own health insurance plan.

As with Mr. Romney, Mr. Giuliani wants to encourage expanded health savings accounts, reform medical malpractice, and improve standards for health information technology.

Whatever the outcome of SCHIP, it’s just a prelude. Mr. Obama and Mrs. Clinton would essentially regulate private plans out of existence, so most Americans would be insured by the new public plans.

Mr. Romney and Mr. Giuliani would remove regulations to encourage more private plans to compete and innovate, and give low-income Americans funds to sign up. Which do you prefer?

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