When organized labor’s most inventive union president and the Republican lawmaker in line to chair the powerful House Ways and Means Committee both tout the same revolutionary idea, it might be time to lend an ear.

Andrew Stern, the liberal president of the Service Employees International Union, and conservative Rep. Jim McCrery, R-La., favored to succeed Rep. Bill Thomas, R-Calif., as head of Ways and Means if Republicans keep control of the House, don’t agree on much.

But both believe it’s time to replace the central arch of the American health care system: the link between health insurance and work. Their arguments might represent the opening notes of the first significant domestic debate of the 2008 presidential campaign.

After President Franklin D. Roosevelt imposed wage and price controls, companies could not compete for workers by offering bigger paychecks. Instead, they provided richer benefits, including health insurance. The big unions bargained for health coverage in their contracts with major employers.

Congress cemented the connection between work and health coverage in 1954 by creating a generous tax subsidy for employer-provided coverage. Employers who provide health insurance for their workers can deduct the cost of the premiums as a business expense. But although workers pay taxes on the wages they receive, Congress decided they would not be taxed on the value of the insurance their employers purchased for them.

That subsidy encouraged employers to shift more of a worker’s total compensation from wages to health benefits. Linking health coverage to work also created insurance pools that shared risk between workers who were young and old, healthy and sick.

With all these advantages, the employer-based system grew enormously over the last half-century. Today, more than 174 million workers and their families receive health insurance on the job.

But as the cost of insurance rises, fewer small employers are offering it. And more large employers claim that the rising cost hurts their ability to compete against companies from other countries that spread the cost more broadly through government-provided health care.

With these pressures, the share of Americans who receive coverage at work has fallen in each of the last five years. Most experts project continued declines. Stern sees in these trends the writing on the wall.

“We have to recognize that employer-based health care is ending; it is dying before our very eyes,” he said at a recent forum sponsored by the Brookings Institution think tank.

Stern flagged the obvious two options: a government-run, single-payer health care regime versus a system that would require individuals to purchase insurance with subsidies from government and, perhaps, mandated contributions from employers. McCrery, not surprisingly, prefers the latter option, minus the employer mandate.

In an essay published this month in the new journal “Democracy,” Jason Furman, a visiting scholar at New York University and former economic policy aide to President Clinton, said that tax policy would be the key to any shift away from the employer-based health care system.

The existing tax subsidy for insurance, Furman said, perversely benefits upper-income workers more than lower-income ones. The reason is that under the progressive income tax, the affluent pay higher tax rates on their income. So it would cost them more than low-income workers if government taxed the value of employer-provided insurance.

Furman says that if government eliminated the current tax subsidy for employer-provided coverage (which costs Washington, D.C., about $200 billion a year), the savings could fund a tax credit that helped all Americans purchase basic health insurance. That structure, he said, would provide the biggest subsidy to the least affluent.

A first step, he said, might be to limit the amount of insurance employers could provide tax free and to use the savings to fund coverage for some of the nearly 46 million uninsured.

Any system that affects as many people as employer-based health coverage won’t be changed quickly, nor should it be. “We have to work incrementally toward getting to a point where we can slowly shift insurance from the workplace,” McCrery said.

Likewise, most big business executives aren’t clamoring to jettison their role.

“We’re not giving up on this system and saying it needs to be thrown out,” said John J. Castellani, president of the Business Roundtable, which represents the nation’s largest companies. “We think it can be improved from both a cost and quality standpoint, and that’s what we are focusing on.”

The critics haven’t assembled an irrefutable case against the employer-based system; refurbishing it might well make more sense than dismantling it. Any replacement system would need to guarantee affordability and preserve the sharing of risk.

But the tough, thoughtful questions from voices such as Stern, McCrery and Furman are an encouraging sign that the nation finally might be ready to re-examine a health care system that costs too much and covers too few.