George W. Bush has a big challenge at the Republican convention in New York. But he also has an opportunity.

The challenge is to change the dynamics of a presidential race that is running against him. Polls show voters are, at best, evenly divided between the two candidates. And the relatively few "undecided" voters are decidedly down on the president. Charlie Cook, one of the few truly independent analysts out there, says only a quarter of undecided voters approve of the job the president is doing. "Ugly numbers for an incumbent," Mr. Cook says. Pollster John Zogby thinks the numbers are even uglier, with just 16% of undecided voters approving of the president's performance.

The opportunity is to present a compelling agenda that establishes him as the candidate of ideas. His Democratic rival, Sen. John Kerry of Massachusetts, passed up that chance in Boston, focusing instead on his biography. That leaves the field clear for the president. If he can give voters a strong sense of what he wants to do with a second term, he just might get one.

The president's call last week for a new era of ownership needs work from the marketing mavens. ("We want more people owning things in this country" isn't much of a rallying cry.) Still, it strikes me as a step in the right direction. The U.S. triumphed in the great struggle of the 20th century because it demonstrated a market-oriented economy with limited government could do more for the "masses" than either communism or the mixed and managed economies of Europe and Asia. For the U.S. to triumph in the great struggle of the 21st century, it needs to prove the point again. And the movement toward a kind of mass capitalism hinted at by President Bush last week could help do that.

The big economic-policy challenge facing the next president isn't how to boost job growth -- that will happen in time -- or how to boost wages -- they will inevitably rise with productivity. The big challenge is how to survive the retirement of the baby boomers, which begins in just five years, without dramatically altering the nature of American society. Left untouched, Social Security and Medicare could cause the U.S. government to swell to 30% or more of the economy from 20%. The welfare state that the U.S. held at bay through the final quarter of the 20th century would expand with a fury. And make no mistake about it: Social Security and Medicare, as now constituted, are a form of welfare.

President Bush's ownership agenda offers the beginnings of a different direction. Social Security could be transformed, at least in part, from a welfare program to a savings plan -- providing all Americans a nest egg that they could own and either use in retirement or pass on to their heirs. The nation's health-care system, which has been insulated from the benefits of the marketplace by a third-party payment system that leaves employers and the government picking up the bill, would be turned into a real marketplace, with consumers owning their own health-insurance plans, making their own decisions about how to spend their health-care dollars, and reaping the benefits of any savings.

Can President Bush sell the American public on such a bold agenda? It won't be easy. With the economy weak and stocks in the doldrums, Americans have lost their enthusiasm for the wonders of the marketplace. Four years ago, more than 40% of voters considered themselves members of the "investor class" -- a sign that a mentality of mass capitalism was already taking hold. Today, says Mr. Zogby, that is down to just 29%.

To succeed, President Bush will have to do a better sales job. And he will have to overcome two strong impressions left by his first term in office.

He will need to show his vision is truly capitalism for the masses, not just capitalism for his cronies. Americans don't like class warfare. But increasingly, they suspect President Bush may be waging it. There is a fine line between eliminating policies that penalize success and embracing policies that unduly benefit the successful. The president is listing over that line.

He will need to show he is willing to make the tough calls necessary to implement his vision. Telling people they can keep some of their payroll taxes in private accounts is easy; telling them the Social Security retirement age is going to rise and cost-of-living adjustments are going to be cut is harder. In his handling of Medicare during his first term, George Bush showed he was happy to give away the candy but had little stomach for administering the medicine. That approach will doom his ownership agenda.

George Bush likes to consider himself the candidate of big ideas. And the ownership agenda he has outlined is very big indeed. The New York convention gives him an opportunity to try and sell it.

Write to Alan Murray at alan.murray@wsj.com ³