BACK IN 1994, the failure of Bill Clinton's health proposal seemed to crush his hope of extending coverage to everybody. Now that hope has bubbled up again, though not from the source that the president might have chosen. On Tuesday Bill Bradley, who is challenging Mr. Clinton's vice president in the Democratic primaries, laid out a scheme that would purportedly extend coverage to nearly all the 43 million-plus Americans who have none. Caught on the defensive, Vice President Gore called for a series of policy debates with Mr. Bradley, with health care high on the list of subjects.

Mr. Bradley's proposal gives the health issue a big boost, since his campaign is gathering momentum. His fund-raising is strong, his poll numbers are firming. Mr. Gore, by contrast, has made a panicky decision to move his campaign headquarters to Tennessee, along with its staff of deeply un-Tennessean strategists. The lesson seems to be that the man with the bold ideas does well, while cautious figures given to fluffy symbolism do not. Location, location, location is a strategy for real estate, not politics.

The health issue's fresh prominence is welcome. Along with the growth in inequality of American incomes, it is one of the few social problems that refuses to improve in the face of prosperity. Crime, teen pregnancy and other social pathologies have receded during this decade, but the number of Americans with no access to health care has grown steadily. This shames a prosperous nation. The question, of course, is how to fix the problem.

Mr. Bradley's fix comes in several bits. It would require parents to buy insurance for children, either privately or from a new range of schemes overseen by the federal government; poor parents would get subsidies to reduce the cost, and the very poor would pay nothing. Next, the Bradley scheme would offer uninsured adults the chance to buy coverage, at attractive group rates, from federally approved schemes; again, the poor would get help to pay for this. Finally, Mr. Bradley promises to make life better for seniors, by adding prescription drug benefits and community care to the existing Medicare system.

Any broadening of the government's role in health risks encouraging employers to give up providing health coverage for employees. It also risks conjuring up vast new bureaucracies and raises budget questions. Mr. Bradley claims that his plan will cost $65 billion a year, and that this money can be found from the budget surplus. The truth is that the plan would probably cost more and that the budget surplus is already being spent in Congress. Mr. Bradley has boldly grabbed a big issue, but the small print of his proposal will inevitably provoke questions.