(FORTUNE Magazine) – When George W. Bush announced that he was running for reelection as Texas governor in 1998, he laid out an audacious goal. He pledged not only to win but to win on his opponents' turf, including El Paso County, one of the largest Democratic enclaves in the state. Although few believed he could do it, Bush prevailed convincingly.

Now, in his presidential bid, Bush is quietly carrying out an El Paso strategy on a national scale. He leads Al Gore in most polls largely because he has focused intensely on winning votes from three groups that usually don't give Republicans more than a sidelong glance: women, Catholics, and Hispanics. If Bush is to beating--Gore with those three groups. It won't be easy. After a plodding post-primary period, the Gore campaign has begun to right itself and is punching back in ways that specifically challenge Bush's strategy. Every time you look, the Vice President is playing Legos with another kindergarten class or making promises to another crowd in a blighted downtown. His campaign believes that the more he empathizes, the more likely it is that women and minorities will vote for him.

Bush will play the empathy card, too, with frequent calls for compassionate conservatism. But his larger goal is to form a new Republican coalition by appropriating the disaffected fringe of the Democratic mainstream, much as Ronald Reagan did in the 1980s. The most vital--and hard to get--cluster of these Democratic voters is women. Bill Clinton became President in large part because he thrashed his GOP rivals among women; in 1996 he carried the women's vote by 16 points. According to the latest polls, Bush is running even with Gore among women. The numbers have caused a minor panic in the Gore camp and are one of the reasons the Democratic Party has begun a $15 million ad campaign to reinvent Al Gore again--this time as a pussycat, not an attack dog. The new TV commercials will portray Gore as a caring young man in his youth and as a friend to the elderly as a politician.

Unlike previous Republican candidates--especially the gang that took over Congress with Newt Gingrich in 1994--Bush will pursue a strategy of being both compassionate and flexible. He'll talk a lot about education and will address grade-schoolers almost as often as adults. He will nod toward gun control, something his GOP predecessors never did; his support of free gunlocks and instant background checks at gun shows is a calculated attempt to appeal to women by distancing himself from the gun lobby. Bush's opposition to abortion is his main obstacle to winning votes from women. He hopes that by rarely speaking publicly about the issue--and by trying to sound reasonable and inclusive when he does--he will lend comfort to undecided female voters. Gore, presumably, will make every effort to call attention to Bush's anti-abortion views.

The Texas governor also has designs on Catholic voters. Ronald Reagan made them part of his coalition, but Clinton captured them for Democrats in the 1990s. About 30% of voters are Catholic, with even higher percentages in key swing states like Michigan, Ohio, Illinois, Pennsylvania, and Wisconsin. The Bush camp believes that if it can reclaim five or six percentage points from the high-water mark Clinton set with Catholics in 1996, (he got more than half their votes), Bush can win those states. So far he outpolls Gore by ten points with Catholics--despite his infamous speech during the South Carolina primary at Bob Jones University, which is despised among Catholics for its anti-papist views.

Bush is not relying on his anti-abortion position to make headway among Catholics. He believes that taking a "catholic" outlook in general will attract that group. When he discusses the need to leave no one behind, to help the least fortunate, to welcome rather than shut out immigrants, and to reverse the moral decline of the Clinton years, he is speaking in large measure to a Catholic audience. On the campaign trail he goes out of his way to visit Catholic community centers, and he has met with five of the eight U.S. cardinals.

Bush hopes his biggest encroachment on Democratic territory will be with Hispanics. He won 49% of the Hispanic vote in Texas in 1998. He also is likely to do especially well among Hispanic voters in Florida, where his brother Jeb is governor. George W. speaks Spanish on the stump and on his Website. There is hardly a barrio in any major state that he hasn't or won't eventually visit. He emphasizes family values, entrepreneurship, and school vouchers, not to mention the close relationship Texas has with Mexico. Republican candidates usually get only 20% of Hispanic votes nationally; Bush is looking for one-third or more, particularly from electoral-rich states like New Jersey, Illinois, and--the big prize--California. Democrats say it will never happen, even though a recent Voter.com poll has Bush trailing Gore by only six points among Latinos. "Bush will succeed in Texas, but he'll fail everywhere else," predicts Democratic pollster Mark Mellman. Bush is determined to prove the pollsters wrong by persuading voters that he really is a new kind of Republican.