(FORTUNE Magazine) – Though Newt Gingrich and his Contract With America led Republicans ten years ago to a historic takeover of Congress, the mastermind behind the conservative ascendancy will not speak at the GOP convention. Nor will you hear his name uttered by any in the current pantheon of party stars. Politics is a brutal business, but even by ordinary Machiavellian standards Gingrich's banishment is striking. "The ingratitude of the right-wing cabal that now controlled the Republican caucus must have galled Gingrich," wrote an analyst recently. "They were in power only because of his brilliant strategy in the 1994 election and his years of organizing and proselytizing before then." A fawning tribute from some Gingrich flack? Nope: Bill Clinton, in his memoir.

Talking with Gingrich is instructive around convention time, if only because four years into the Bush era, you almost forget that Republicans once had their own Clintonesque hybrid of hyperarticulate policy wonk and ruthless pol. Looking fitter at 61 than a decade ago as a portly firebrand, Gingrich still spins big visions, if now from a modest office on K Street. His current passion for reforming health care may sound as improbable to his fellow Republicans as--well, as his insistence in the 1980s that the GOP could one day control Congress. "The Republican Party has an opportunity to end up owning health as an issue," he says with characteristic certitude.

Gingrich has focused on health care in his post-congressional life because, he says, it's "the largest sector of the economy and the area where it's easiest to make very large gains in productivity." He launched the Center for Health Transformation, a for-profit research and consulting group, after he and his team scoured the country to detail the system's ills and potential cures for a 2003 book, Saving Lives and Saving Money. On the lecture circuit, in Hill testimony, and when counseling corporations, he uses well-honed riffs. "When you tell people that you're 2,000 times more likely to die in the hospital from a mistake than in an airplane, people get it," he says. When you remind them that they travel with an e-ticket, a cellphone, and a BlackBerry, he adds, and then ask why prescriptions are still scribbled illegibly (and dangerously) by doctors on paper, they shake their heads. "The gap between normal commercial behavior and health care" is huge, Gingrich says.

So far, so bipartisan. But beyond his crusading for industrywide IT and against deadly medical errors--areas in which he makes common cause with erstwhile foes Hillary Clinton and Ted Kennedy--Gingrich believes that market-oriented reforms can deliver better care for less cost while helping conservative politicians. He hardly invented the notion of consumer-driven health care, but he's its shrewdest political evangelist. Much of his agenda is uncontroversial--good data on quality and outcomes so that patients can make smarter choices, a fresh focus on wellness and prevention as opposed to acute care, and so on. But the centerpiece is a call to put consumers (not third-party insurers) in control of more health spending via widespread adoption of health savings accounts (HSAs). Here the battles are just beginning.

Gingrich practically begged conservative lawmakers to pass Bush's Medicare bill, despite their fears of its pricey drug entitlement, precisely because the bill also authorized HSAs. The provisions were little-noticed outside the industry, but Gingrich believes they are the most important lever available to transform the system--and a potent goody for Republicans on the stump.

Tax-deductible HSAs allow wage earners to set aside up to $2,600 (for individuals) and $5,150 (for families) each year. Employers may also choose to fund HSAs on their employees' behalf. The money can be drawn on for medical expenses; unused balances can be accumulated and invested tax-free. The catch is that you are eligible for an HSA only if you also have a health-insurance plan with a high deductible--at least $1,000 a year for an individual and $2,000 for a family. Advocates hope the combination will finally bring consumer pressures to bear on routine health expenses, so that market forces start reining in spiraling costs. Insurers are now racing to roll out HSA high-deductible offerings in 2005. Banks and other asset managers are poised to enter the market as well.

To liberal critics HSAs embody two classic GOP sins. First, they drain the Treasury to give people another tax-sheltered savings vehicle (no wonder Gingrich expects many voters to cheer). Worse, since HSAs seem likely to attract people who can afford to deal with high deductibles and people who expect lower medical costs, they'll fragment the risk pool and doom sicker, poorer Americans to policies whose premiums will soar--or to living with no insurance.

When I ask about those concerns, Gingrich asserts, too glibly, that they won't be an issue. The former speaker, whose daughter has suffered from rheumatoid arthritis from an early age, also bristles at the notion that he doesn't care about the unwell. "I believe in true insurance," he says, which means "collectively joining together so that those of us who have bad luck, whether it's a physical accident or a genetic problem, are carried by the totality of the system." What he doesn't believe in, he says, is "prepaid normal care," which lets people be oblivious to routine health costs. The savings employers reap by providing high-deductible policies, Gingrich adds, may lead them to fund big chunks of lower-income workers' deductibles via their HSAs. And if liberal fears of risk-pool fragmentation do come to pass, Gingrich tells me, "we should modify the cross-subsidy to assure that it doesn't happen."

"So you're in favor of redistributing wealth to the unlucky in health care?" I ask, wanting to be clear.

"Absolutely," Gingrich says. "I'm perfectly happy to have redistribution when it's needed," he adds later, saying this need goes beyond health insurance to areas like government funding of savings accounts for poorer children at birth.

From a business perspective, the deeper flaw with HSAs is that they can't address the real cost problem. To be sure, if millions of routine health encounters are paid for by patients directly, some prices may come down, and billions in processing fees between providers and insurers could disappear. But 80% of health costs come from the costliest 20% of cases, and those involve bills that far exceed any HSA deductible. Gingrich acknowledges that and says you can't expect HSAs to solve everything. Yet he also thinks that they may reshape people's thinking about high-cost cases.

"Imagine a union contract that said you get to pick the size of your deductible and that relates directly to the amount of your take-home pay," Gingrich says. "So if you've built up a $30,000 HSA over the last ten years and you'd like to risk a $30,000 deductible, your employer might say, 'We'll increase your take-home pay this year by $2,600 because you'll save us in premiums.' Now you've just changed the whole point at which people make those kinds of decisions."

That's Newt being Newt--intriguingly outside the box, and if you're a Republican politician, outside the comfort zone as well. Already the party is taking lumps on the prescription-drug bill it thought would be a winner. Does Gingrich really think the GOP can steal health from the Democrats in the next decade? "It's still very hard to get this party to be comfortable explaining complex domestic policies," he says. "It's not how they get elected. You're asking people to irritate their own [antigovernment] base to create a larger majority."

Yet Gingrich thinks the party can get there. "What I say to conservatives is simple: You will never balance the budget if you don't transform health. And if you don't want to see your children and grandchildren crushed by massive tax increases when the baby-boomers retire, you had better transform Medicare." There's a national-security imperative too, he says: America needs a 21st-century public-health system to deal with the threat of bioterror. "I have a different level of confidence about talking directly to the base" on these subjects, Gingrich adds. "When I do it, they applaud."

Later, in a windowless basement auditorium under the Capitol, 200 congressional interns listen raptly as Gingrich, ever eager to indoctrinate the young, previews his forthcoming book. Due out in January, it will offer--what else?--a 21st-century Contract With America. It's about large generational challenges, a presidential-style agenda.

Does he dream of a comeback? I ask. "It doesn't strike me as plausible," Gingrich says, a little wistfully. Gingrich e-mails Karl Rove on strategy. His advice is sought by congressional committee chairmen. He sees his electoral exile as the inevitable result of 125,000 ads that ran against him unanswered in the 1996 campaign, forever destroying "Newt Gingrich" as a political brand.

"You have to be realistic," Gingrich says of speaking at the convention. "If I were the Bush administration and my choice was Schwarzenegger, Giuliani, McCain, or Gingrich, I'd put me fourth."

MATTHEW MILLER (www.mattmilleronline.com) is a senior fellow at the Center for American Progress and author of The 2% Solution: Fixing America's Problems in Ways Liberals and Conservatives Can Love.