Presumptive Democratic presidential nominee Barack Obama says he would achieve universal health coverage by the end of his first term in the White House. He asserts that his proposal would save $200 billion a year in health-care spending and reduce the average family’s medical premiums by $2,500 a year. The found money would go to cover the 47 million uninsured Americans and cut the premiums of struggling families. Admirable goals and impressive numbers, but are they real?

Probably not. Let’s take a look.

The most problematic number is the $81 billion that would allegedly be saved by improving prevention programs and chronic-disease management. From a quality-of-life standpoint, both are desirable goals. But prevention programs — such as helping people stop smoking or lose weight — don’t save money in the long run.

Starkly put, people with poor health habits die younger and so spend less time on Medicare (where they are covered for the very expensive ailments of old age). An article in the February New England Journal of Medicine reports that only about 20 percent of preventive measures actually save money. The problem, medical economists say, is that preventive care is given to many who wouldn’t have gotten the illness it seeks to avoid. And it goes to others who would have gotten the illness anyway.

Chronic-disease management, say, for diabetes, could save money if it kept people out of the hospital. Depression, on the other hand, is a chronic illness for which few of the afflicted are hospitalized. From a health standpoint, depression is something that definitely needs treatment. But it can’t be said that treating depression reduces medical spending.

The Obama plan holds that another $77 billion would be saved though computerized medical records. That number, from a RAND Corporation study, has been questioned by the Congressional Budget Office as too large.

The proposal would largely rely on private insurers to continue covering the masses, although it envisions a new government-run plan to compete with the private options. The insurers would be required to offer a certain level of benefits and, according to the Obama Web site, “charge fair and stable premiums that will not depend upon health status.”

Whether these new rules would shave $46 billion off administrative costs, as Mr. Obama claims, is anybody’s guess. But we wonder how eager private insurers would be to sign up sick people at fixed premiums — especially since the Obama plan lacks a mandate requiring everyone to obtain coverage. That means young and healthy people could avoid buying insurance at all, leaving a medically expensive base of enrollees.

If the Obama plan sounds complicated, that’s because it is. We haven’t gotten into the parts about expanding various subsidies for low-income people, tax credits for small businesses, required payments by large employers that do not cover their workers, and a program to help company health plans burdened by the catastrophic illnesses of their workers. There’s a strong sense here that the big-spending lobbyists of the for-profit health-insurance industry have gotten to Mr. Obama, as they get to most Washington luminaries.

But if one truly wants to lower administrative costs, why not expand Medicare to all? Medicare has tiny administrative costs. A single government-run plan that provides the basics and lets people buy private coverage for the extras would be simple to administer and to understand. It ends the illogical and grossly unfair tradition of employer-based coverage and brings healthy people into the risk pool.

Given the furious debate about government-run health programs (though most beneficiaries like them), we can understand why Senator Obama would be hesitant to embrace the idea. But it seems doubtful that his proposal would achieve nearly the savings it claims, and it’s awfully complicated. Universal coverage is essential. Let’s keep working on this.