Common wisdom has it that, after the Clinton administration’s disastrous health care reform of 1993, Congress could not look at the subject again comprehensively but would have to content itself with incremental change. Fortunately, common wisdom is like the common cold – most people get it and then get over it.

Conservative Rep. Jim McCrery, a Republican from Louisiana, got over the conventional ideas about comprehensive health care reform this way: The current incremental approach, he has concluded, is leading the nation inexorably toward a government-run, single-payer health plan. Exactly where he does not want it to go, but where the country will end up unless Congress passes major reform to include the 43 million Americans who currently lack coverage.

In an extraordinary interview in this month’s Atlantic Monthly, columnist Matthew Miller sat down with Rep. McCrery and Rep. Jim McDermott, a liberal Democrat from Seattle, colleagues on the House Ways and Means Committee subcommittee on health care. With Mr. Miller’s prodding, the two hashed out ways of delivering universal health care in a way that could attract support from both parties. While the interview didn’t work its way down to the details of what sort of benefits would be offered, it did outline how coverage might be delivered affordably to all Americans.

Some highlights worth considering:

Rep. McCrery would support means-tested tax subsidies to provide everyone with coverage. Using the federal-employee health plan as a model, the coverage would not be defined for every test and procedure, but would assure coverage in medical areas such as surgical and major medical expenses. But ultimately, points out Rep. McDermott, “there has to be a come-to-Jesus meeting someplace where the package is defined.”

Getting everyone covered means providing insurance at a price everyone can afford, which leads to community rating – charging everyone the same price regardless of sex, age or medical history. Employees of companies with group plans are under a kind of community rating now, but people buying individual policies can be subject to extremely high insurance prices if they are likely to use the insurance. Rep. McCrery says: “Yes, you can have a high-risk pool, with people moving from under the red line to above the red line, but why fool with all that? It’s complicated, it’s troublesome, it distorts the market. Why not just have community rating and then let insurance companies compete on the basis of value?”

A government tax subsidy to purchase insurance, both men recognized, would encourage businesses to drop coverage and let government pick up the tab. Rep. McCrery advocates letting each company “cash out” its employees by distributing the money it paid in health care as wages, enabling employees to take the extra money to buy a health plan. But the big question remained: What do you do with employees who do not currently receive a health-care benefit? The answer, they say, is to scrap the current tax subsidy “under which employers can deduct health-care expenses from their taxes but employees don’t have to include the value of those benefits in their taxable income,” explains Mr. Miller. This current system provides a $125 billion-a-year subsidy that most highly rewards those with the very best health plans.

This final idea is politically perilous to Rep. McDermott because unions, some of his strongest supporters, use this break to underwrite valuable health plans. In the interview, the congressman talked about the issue for a bit, no doubt thought of his own re-election this fall, then said, “I would not reject this idea.” That’s a large concession on a tough subject.

It is hardly the only concession both sides would have to make to assemble a working model of health-care insurance that covers everyone, but it is proof that, for political leaders who study this problem closely, the various sides are not permanently split. They could put together universal coverage with wide support by changing the way care is paid for. The alternative, they know, is a knocked-together piecemeal system that few, in or out of Congress, would end up supporting.