First, the uninsured are disproportionately young adults, whose medical costs tend to be relatively low. The big spending is mainly on the elderly, who are already covered by Medicare .

Second, even now the uninsured receive a considerable (though inadequate) amount of “uncompensated” care, whose costs are passed on to the rest of the population. So the net cost of giving the uninsured explicit coverage is substantially less than it might seem.

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Putting these observations together, what sounds at first like a daunting prospect — extending coverage to most or all of the 45 million people in America without health insurance — should, in the end, add only a few percent to our overall national health bill. And that’s exactly what the budget office found when scoring the HELP proposal.

Now, about those specifics: The HELP plan achieves near-universal coverage through a combination of regulation and subsidies. Insurance companies would be required to offer the same coverage to everyone, regardless of medical history; on the other side, everyone except the poor and near-poor would be obliged to buy insurance, with the aid of subsidies that would limit premiums as a share of income.

Employers would also have to chip in, with all firms employing more than 25 people required to offer their workers insurance or pay a penalty. By the way, the absence of such an “employer mandate” was the big problem with the earlier, incomplete version of the plan.

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And those who prefer not to buy insurance from the private sector would be able to choose a public plan instead. This would, among other things, bring some real competition to the health insurance market, which is currently a collection of local monopolies and cartels.

The budget office says that all this would cost $597 billion over the next decade. But that doesn’t include the cost of insuring the poor and near-poor, whom HELP suggests covering via an expansion of Medicaid (which is outside the committee’s jurisdiction). Add in the cost of this expansion, and we’re probably looking at between $1 trillion and $1.3 trillion.

There are a number of ways to look at this number, but maybe the best is to point out that it’s less than 4 percent of the $33 trillion the U.S. government predicts we’ll spend on health care over the next decade. And that in turn means that much of the expense can be offset with straightforward cost-saving measures, like ending Medicare overpayments to private health insurers and reining in spending on medical procedures with no demonstrated health benefits.

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So fundamental health reform — reform that would eliminate the insecurity about health coverage that looms so large for many Americans — is now within reach. The “centrist” senators, most of them Democrats, who have been holding up reform can no longer claim either that universal coverage is unaffordable or that it won’t work.

The only question now is whether a combination of persuasion from President Obama , pressure from health reform activists and, one hopes, senators’ own consciences will get the centrists on board — or at least get them to vote for cloture, so that diehard opponents of reform can’t block it with a filibuster .