(FORTUNE Magazine) – House Republicans are hopeless, literally. Also rudderless. And desperate to recover from the impeachment debacle. They're craving adult supervision. Not for nothing did they summon the onetime head of the National Wrestling Congress for help. So now that Dennis Hastert--not identified with any big idea, trend, or accomplishment--is Speaker of the House, Republicans, whose only motivation was to find a leader who was Not Newt, are left worrying whether they have neutered the office of Speaker.

Luckily for the GOP, there's more to Denny Hastert, 57, than not being Newt. Heir to luminaries like Henry Clay, John Nance Garner, Sam Rayburn, and Tip O'Neill, this unknown Illinois lawmaker is quietly transforming how the House works. Here's the most stunning pronouncement yet from the new Speaker: "My mantra is that we get our work done on time." No grand overhauls of society. No grand quotes from Edward Gibbon or Alvin Tofler either. Just a budget before summer, 13 appropriations bills by August, maybe a tax cut in the fall, perhaps some regulatory reform. Small bites, not the whole apple. "It doesn't matter that he's not a high-profile guy," Representative John Sununu of New Hampshire says of a man whose colleagues call him "Coach." "He's a high-trust guy. That will make all the difference."

So far it has. Gingrich, who taught college history, had an opinion on everything and loved to talk about creating a new civilization. Dennis Hastert, who taught high school civics, keeps his views to himself and would be content to bring some civility to the House. Gingrich was a master of the physics of repulsion; he gathered acolytes like a magnet, only to erect a force field that kept away Democrats, the White House, business, and the public. Hastert is insisting that major initiatives have Democratic support before they're sent through committee; as a result, the House has been remarkably quiet as Republicans romance Democrats on appropriations bills and even on taxes. Gingrich was obsessed with figuring out why the Middle Ages ended and why Confucian China collapsed, all with an eye toward propelling America onto the next wave of history. Hastert would like to know whether it's possible to delay the way OSHA promulgates regulations, and if so, he'd like some Democratic co-sponsors.

This may not sound like a radical departure, but it is. Think of it as the return of your father's Congress. Hastert actually considers Bob Michel, the old-school House GOP leader whom Newt sought to erase from history, one of his closest confidants. Sure, there are plenty of firebrands still in the Republican cloakroom. But with a measly six-seat majority, Hastert couldn't be daring even if he had the inclination. His strategy, born of his temperament and the GOP's predicament, is: Don't alienate anybody. The Speaker is quietly talking to New York PR firms to help his party clean up its image. "The people who sell soap will help them sell their ideas," says David Rehr, a beer wholesalers' lobbyist with close ties to the GOP leadership. "The last time they tried selling something, they had Newt standing in front of the Capitol with a stick of dynamite."

The Speaker, meanwhile, is going to nearly every GOP congressional event, putting together a big war chest to do the one thing--maybe the only thing--every Republican believes in: getting reelected and keeping control of the House. What they don't show in vitality and earn in legislative achievements, members of the House GOP aim to make up in money. Under Dennis Hastert, the Republicans are looking beyond the general crisis in post-industrial society and are worrying about the collection plate. It's a strategy that seldom fails on Capitol Hill.

DAVID SHRIBMAN is Washington bureau chief of the Boston Globe and a Pulitzer Prize-winning political reporter.