President Bush has long pursued a calculated strategy to build a lasting Republican majority, coupling courtship of the party's conservative base with efforts designed to attract support from Hispanics and targeted swing voters. But rarely have the two sides of this strategy been in such conflict as they are today with the possible nomination of Attorney General Alberto R. Gonzales to the Supreme Court.

Well before Bush makes his decision known, a fierce battle has erupted over Gonzales, the former White House counsel and Texas Supreme Court justice. It pits the ideological priorities of social and religious conservatives, who think Gonzales is insufficiently opposed to abortion, against the aspiration of the Latino community to see the first Hispanic named to the high court.

Bush has skillfully balanced his appeals to both groups throughout his career as an elected official, but he faces the prospect of disappointing one side, with potentially serious repercussions for his party.

Nothing prevents Bush from trying to skirt the conflict by naming another Hispanic who would be more acceptable to the right than Gonzales, such as Emilio M. Garza, a judge on the U.S. Court of Appeals for the 5th Circuit. But the uproar over Gonzales, longtime friend and confidant of the president, has heightened the political stakes of Bush's decision and has alarmed some senior GOP strategists.

Whichever way Bush moves, his decision is likely to be interpreted in part through the prism of the argument over Gonzales that precedes the announcement of a successor to retiring Justice Sandra Day O'Connor.

After Bush pointedly complained about the attacks on Gonzales, critics on the right have grown more tentative in directly criticizing the attorney general. But they cannot mask their unease about his possible nomination to the Supreme Court. Hispanic leaders are equally clear about their resentment over attacks on Gonzales.

"We don't like it, and we'll have to deal with it as it unfolds," said Hector Flores, president of the League of United Latin American Citizens. He added that many Hispanics think this nomination should be Gonzales's. "We feel very strongly that Alberto Gonzales should be the first one to bat," he said.

All this may be premature, given that only a handful of people know who is on Bush's list of possible nominees. But the conservative criticism of Gonzales has alarmed some GOP strategists, although they are reluctant to inject themselves publicly into the middle of the fight before Bush makes a decision.

"There is a lot of grumbling about this, about whether we seem to be catering to just one side of the party," said one Republican strategist. "We need to be inclusive to all. If it's 'our way or no way' [among social and religious conservatives], that's really not a party."

Bush's political project, which he shares with his chief political adviser, White House Deputy Chief of Staff Karl Rove, has moved the party close to the kind of dominance Republicans and conservatives have worked toward for more than three decades. It rests on a foundation of rock-solid support among conservatives -- economic, social and religious -- and often has been seen as little more than that.

But between 2000 and 2004, Bush was successful in expanding GOP support at the margins among others outside that base, from Roman Catholics to women to Hispanics. Noting that Bush got 11.6 million more votes in 2004 than in 2000, Rove told Washington Post editors and reporters this week, "It's a misread to suggest that we got that by appealing to the base."

Asked whether Gonzales fits the mold of Antonin Scalia or Clarence Thomas, whom Bush has cited as examples of conservative justices he admires, Gary Bauer of the Campaign for Working Families said: "Only the president can answer that."

Tony Perkins of the Family Research Council was equally deflective when asked about Gonzales's views, but he did note that "I think there will be a problem within the coalition" if Bush fails to nominate a genuinely conservative justice.

Among political strategists, there was disagreement yesterday over whether Bush risks rupturing that coalition and thereby damaging his longer-term political project with his choice.

Simon Rosenberg, founder of the New Democrat Network, said the decision comes at a time of growing strain in the GOP coalition. "You're seeing the kind of public fighting inside the Republican Party that didn't happen a few years ago," he said. "This year has been the toughest year in their coalition since they won the Congress in 1994."

Democratic pollster Sergio Bendixen, who is working with the liberal group People for the American Way in the court fight, said Bush's standing among Latinos -- the president won just over 40 percent of the Hispanic vote in November -- means the fastest-growing segment of the population is no longer clearly part of the Democratic coalition but a competitive swing vote.

But he said that the uproar over Gonzales could turn off many Hispanic voters and push them back toward the Democrats. Recalling the Latino backlash to the fight over illegal immigration in California launched a decade ago by then- Gov. Pete Wilson, he said Bush and his advisers "need to keep control over that right fringe that put California in the blue [Democratic] corner for a generation."

Republicans offered differing views about what Bush's choice may do to his coalition. Pollster David Winston said he believes that Bush could nominate someone with Gonzales's views without causing major problems on the right. "This is a president who . . . has had very solid and significant support," he said. "It's a base that's willing to go a long way with him."

Sean Rushton, executive director of the Committee for Justice, a group formed to support Bush judicial nominations, questioned whether a conservative nominee would alienate moderates. "That's nonsense," he said. "The worst thing the president could do for his party's 2006 election hopes -- and especially for [Sen.] Rick Santorum in Pennsylvania -- is to go with a nominee who is seen as less principled by conservatives. That would completely dry up the funding. That would completely dry up the enthusiasm."

Henry G. Cisneros, who was housing secretary in the Clinton administration and who supported Gonzales's nomination as attorney general, said the biggest payoff for Bush could come by naming a Latino other than Gonzales, namely Garza. "Bush would get credit from Latinos for naming the first Latino to the Supreme Court and [have a nominee] who is not anathema to the far right," he said.

Cisneros said he doubts that Bush will pass up the opportunity to name a Latino to the court, whether with this choice or the next one. "It's too big an opportunity not to do it," he said.

Whether Bush sees himself as being in a bind, only he and his advisers can say. But the longer he goes without naming a successor to O'Connor, the more the debate over Gonzales is likely to fester.