The battle to define Texas Gov. George W. Bush begins this week.

Is he a compassionate conservative or a presidential candidate unwilling to offend his party's right-wing constituencies? Is he a decisive leader or a politician who doesn't know his own mind? Is he an aging Baby Boomer who has outgrown his youthful indiscretions or a politician still haunted by his past?

As Bush shifts his focus from Texas to the national stage in the coming days, both his campaign team and Democrats who see him as the GOP's most formidable nominee will be engaged in a high-stakes competition to shape public perceptions of candidate Bush.

Even before Bush's first campaign trip, two Democrats who will play leading roles in Campaign 2000 -- Vice President Gore's campaign chairman, Tony Coelho, and the Democratic Party's general chairman, Roy Romer -- questioned Bush's fitness to be president. Their comments, in separate interviews, showed that Democrats would give no free passes to the governor, even though the GOP nomination is months from being settled.

"The issue as I see it is: Is he ready for the major leagues?" Coelho said. "He's been playing in the minor leagues, but they've hyped it as if he's been in the majors. He's got this team of people who say he's the savior of the major leagues. . . . Al Gore has played in the major leagues."

The Democrats' determination to crash Bush's coming-out party underscores how eager they are to prevent him from getting a fast start as a presidential candidate. Democrats around Gore, who has been struggling to put his campaign on track, appear especially worried about the Bush threat.

"Gore's team seems totally and completely obsessed with him," said one congressional Democrat. "They never call and say what can you do to hit Bill Bradley or Liddy Dole. They're very focused on George W. and dragging him down."

If Bush's advisers hoped to ease him onto the campaign trail in June, they may be in for a rude awakening. Not only will the governor be chased by a Texas-size pack of reporters eager to elicit his views on scores of topics, Democrats will be lurking as well. The DNC has been laying plans to challenge Bush on his initial trip, and Coelho said as the time comes closer, Gore may do the same.

Bush press secretary Karen Hughes said Bush would talk about broad themes but doubted "that he will have a 10-point plan for any subject." Mostly he will spend time "shaking hands and taking pictures and hugging and meeting people."

Democrats have other ideas. They hope to shift the focus to social issues, gun control and what they say has been Bush's shaky performance on issues such as Kosovo.

"Democrats should be raising issues that put him on the spot, whether it's Kosovo or guns or abortion," said Democratic pollster Stan Greenberg. "The issues that divide Republicans should be the ones Democrats highlight and ask about. Democrats should do the job that Republicans appear reluctant to do."

Romer, a former governor of Colorado, said Bush has displayed extreme caution as a candidate, not the kind of bold leadership his supporters claim. "He has been ducking a number of issues -- deliberately it would appear -- and I don't think that stands him well in a presidential race," Romer said.

Romer said Bush has been a less distinguished leader than many other Republican governors, adding, "If he didn't have that name, he would not be the front-runner. He might not even be in the race."

"We are observing closely," Romer said. "Kosovo, he took a bye. Background checks on gun shows, he took a bye. On hate crimes, he chose to be silent. If you really want to be the leader of this country and the free world, you've got to be willing to call balls and strikes and not hide from them."

Bush advisers dispute those criticisms, saying Bush has made himself clear on major issues that have arisen this year.

Even though there are nearly a dozen Republican presidential candidates, Democrats have made Bush their principal target in part because they fear that the GOP establishment is forming a protective cocoon around the governor long before he has competed in his first primary.

Democrats also hope to force Bush to defend congressional Republicans, who departed on recess once again in disarray. Noting that half of the House Republicans already have endorsed Bush, a DNC official said, "If they want to put all their eggs in one basket, we'll do everything we can to show what's in that basket and whether the person entrusted in carrying it is up to the job."

Gore's concern about Bush is obvious, given the fact that the Texas governor's lead in the polls has made many Democrats nervous. Gore is actively considering moving up his formal announcement from September to early summer, but Coelho insisted that the decision had nothing to do with the beginning of Bush's campaigning.

Still, Coelho's willingness to outline areas of criticism indicated that Gore's advisers have been closely monitoring Bush's activities. He too questioned Bush's handling of Kosovo and said that, on the issue of Chinese espionage, Bush has opened the door to a discussion of what happened when his father was president and vice president and whether steps should have been taken to prevent security breaches. On guns and abortion, he said, Bush has revealed himself to be "captive of the right" in the Republican Party.

In the wake of the Littleton, Colo., school shootings, Democrats say Bush has sided with the gun lobby because he said if he were president, his vice president would not have cast the tie-breaking vote in the Senate on new gun control legislation, as Gore did. But Bush spokesman David Beckwith said the fight is over the fine print of the law, not the principle of background checks for purchasers at gun shows. "The DNC is being disingenuous," he said.

Hughes said with a laugh that Bush's team would rebut Democrats "as best as we can." But one Bush adviser expressed fears that a concerted Democratic attack this early in the campaign could create problems that will take months to overcome. Democrats, this adviser said, will attack Bush as too light and inexperienced to be president while trying to pick him apart on specific issues. "The fact is, he's not light," the adviser said. "He's a very bright guy. But through sheer repetition it can be a problem."

The character issue presents a more delicate question for Gore and the Democrats. Bush has acknowledged heavy drinking and youthful indiscretions but has refused to answer specific questions, particularly about whether he ever used drugs. He has insisted that nothing he did as a youth disqualifies him to be president.

Some Democrats close to Gore are known to believe that Bush's past will become a central issue in the Republican primaries and that, over time, Gore will be able to contrast himself favorably with the Texas governor on character issues. When Coelho heard that, he called a reporter to angrily deny that such thinking represented Gore campaign strategy. "Al is not interested in that type of campaign or that type of issue," he said. "There has been no discussion whatsoever, and I will not permit it. This is not where we are."

But Coelho later predicted that Bush will be confronted by more direct questions about his past from the news media and particularly in debates with other GOP candidates, and added, "There's none of those questions Al hasn't been asked, and Al's answered those questions."

Republicans, however, said any Democratic attempts to invoke character would backfire because so many Democrats defended Clinton over his relationship with Monica S. Lewinsky. "Not only will the hypocrisy be transparent, but there will be a boomerang effect," said Tom Cole, chief of staff at the Republican National Committee. "The Democratic Party has lost the credibility to question anybody's moral character or background. If they try, it will be crazy."