(FORTUNE Magazine) – A tuxedo-clad Republican leaned across the linen tablecloth and whispered, "He's George Bush's worst nightmare." This Washington insider wasn't referring to Al Gore, Tom Daschle, or Dick Gephardt. Everyone knows they'll pose problems for the next President. He was talking about Tom DeLay, a fellow Republican and the most powerful man in Congress. George W. needs DeLay, the House Majority Whip, to get anything done on Capitol Hill. In the House, DeLay is DeLaw. But the two Texans don't get along personally or politically, and there's no guarantee they ever will.

The nation's capital may be even more divided than the rest of the country. No legislation can possibly move unless Republicans and Democrats figure out a way to work together. Most observers believe the difficult part for Bush will be persuading moderate Democrats to ally themselves with moderate Republicans. In fact, the tougher task will be to keep the GOP's hard right, led by DeLay, from bolting when Bush inevitably pushes his policies leftward to gain Democratic support. "As President, Bush will need to achieve results," says Marshall Wittmann, an ex-Christian Coalition lobbyist now at the Hudson Institute. "He will need to strike compromises with Democrats that will endanger his relations with conservatives. Bush will have to walk a very thin line."

As the House's third-ranking Republican, DeLay follows Speaker Dennis Hastert and Majority Leader Dick Armey. But that understates his clout. Two years ago DeLay all but selected Hastert--then DeLay's deputy--as Speaker after the demise of Newt Gingrich and Bob Livingston. DeLay could have been Speaker himself, but he realized that his vicious anti-Clinton views made him politically radioactive. DeLay also might have become the House's liaison to the Bush campaign, but for similar reasons he blessed his current deputy, Roy Blunt of Missouri, for the job.

There's another reason DeLay chose not to speak for Bush: They don't much like or trust each other. In casual conversation with other House members, Bush has used barnyard slang to disparage DeLay. DeLay has been equally uncharitable in private about Bush. In 1999, Bush accused DeLay-led Republicans of trying to "balance their budget on the backs of the poor." DeLay shot back that Bush "doesn't know how Congress works." DeLay admitted to the New York Times that he and Bush had "never had dinner. We aren't social friends."

They come from different worlds. Bush is an ivy-educated patrician eager to accommodate in order to succeed. DeLay is a former termite exterminator so zealously ideological that he recently said he was willing to shutter the government rather than acquiesce to President Clinton's increased-spending proposals. Bush aspires to unite, not divide. DeLay revels in division; he nicknamed himself the Hammer.

The rivalry goes back years. In 1989, DeLay tarnished his bona fides as an archconservative by opposing Gingrich for House GOP Whip. DeLay recouped his standing the next year at the expense of George W.'s dad; he was one of the first Republicans to attack the tax increase embraced by President George H. W. Bush in 1990. The resulting invective from the right was a leading cause of the elder Bush's 1992 defeat. Aides say his son will never forget.

At the same time George W. knows he needs DeLay. The wily Whip has assembled the House's most extensive and disciplined vote-gathering operation in two decades. No one is under the illusion that Bush's conversations with Hastert and Senate Majority Leader Trent Lott will amount to much if DeLay disagrees. And that's a problem in itself. What self-respecting Democrat would accept a "compromise" approved by a fire-breather like DeLay--who may be more despised by Democrats than Gingrich was? Even the House's most conservative Democrats, the so-called Blue Dogs, are reluctant to deal with DeLay. They have urged Bush to devote half the budget surplus to debt reduction and a quarter to tax cuts--the reverse of DeLay's priorities. Bridging this divide, says GOP Representative Jennifer Dunn of Washington State, "will be a fascinating challenge for Bush."

At first DeLay will probably cut the President-elect some slack. Advocates for both men say they agree more often than they're given credit for. For instance, both favor easing the marriage penalty and reducing estate taxes. They also understand that their ability to collaborate may determine whether voters keep the Republicans in charge after the 2002 and 2004 elections. "It will take a little effort [for them] to develop" a closer association, concedes Representative David Dreier, chairman of the House Rules Committee. But develop one they must, or it's curtains for the Bush Administration.