Sen. Chuck Hagel (R-Neb.), a man known for frank talk, offered a blunt description of the state of his party, which broke camp here Friday after nominating President Bush for a second term. "The Republican Party," he said, "has come loose of its moorings."

Hagel was not referring to Bush's leadership or his prospects for reelection but instead to the impact of a presidency that has seen the party embrace the largest deficits in U.S. history and a foreign policy that has put the United States at odds with many of its closest allies and heightened suspicion of institutions such as the United Nations.

Hagel expects recrimination and worse if Bush loses to John F. Kerry, but he predicts that, win or lose, the GOP faces a period of introspection and debate over its future. "I think you've got a party that is in a state of uncertainty," he said.

While many Republicans attending the convention dismissed Hagel's prediction as unduly pessimistic, there is likely to be a series of intraparty debates, starting after the election, over the size and role of government, the U.S. role in the world, and how Republicans can expand their coalition.

Some Republicans believe that, if Bush is reelected, a second term will put a fresh face on the party and resolve some festering disputes. "I just don't feel that . . . a lot of these disputes between deficit hawks and supply-siders or between social and economic conservatives are going to create nearly the level of fissures or the number of fissures that they might have in the past," said Ralph Reed, former chairman of the Georgia GOP. "I think it's very hard to go back as a party once you've had a transformational figure."

Yet Reed's conclusion is the opposite of the argument Republican speakers advanced throughout their convention, as they portrayed Kerry as a Democrat who would take the country back to a pre-Clinton liberal mind-set. Whether that is true or not, Democrats learned after the Clinton presidency and Republicans learned after eight years of Ronald Reagan that seemingly settled arguments suddenly reappear and that parties regularly face internal warfare over their direction.

The future of the GOP will be shaped by party intellectuals, think-tank fellows and constituencies seeking to alter the balance of power within the party, as well as by battles in Congress over spending and taxes. But added to that is the battle for the party's 2008 presidential nomination. With Vice President Cheney already ruling out a run for the presidency, there is no heir apparent.

Throughout the convention week, prospective candidates diligently made the rounds of delegation caucuses, with the Iowa and New Hampshire delegations particular favorites, and several of the party's brightest stars who might be candidates -- particularly Sen. John McCain (Ariz.) and former New York mayor Rudolph W. Giuliani -- lit up Madison Square Garden with their speeches.

Change will also come from outside forces, most notably two powerful demographic trends that will have an impact on both parties -- the coming retirement of the baby-boom generation and the rapid growth of the Latino population.

The boomers' retirement will strain the government's ability to fund Social Security and Medicare and will heighten the debate within the party about the federal deficit. "The day of reckoning is getting closer," said John J. Pitney of Claremont McKenna College in California.

The growth of the Latino population threatens to reshape the presidential electoral map in the Democrats' favor unless Bush and others in the GOP begin to increase their share of the vote in a constituency that remains strongly Democratic. That task is complicated by the traditional Republican instinct -- heightened in this security-conscious era -- to be tough on immigration. Still, Republicans say Hispanics should be attracted to the party's conservative values.

While Republicans have rallied around Bush's leadership, a defeat in November will probably trigger a major reassessment of where the party went wrong. On both fiscal policy and foreign policy, Bush has defied the instincts of a significant segment of the party. Deficit hawks have been in retreat, as have those who favor realism, not moralism, in foreign policy.

"The interventionists in the party will be in trouble," Pitney said. "If Bush goes down, so will Wilsonian rhetoric. A lot of Republican thinkers are going to be dusting off their Henry Kissinger books."

Hagel, who has differed with Bush on Iraq and foreign policy, sounded ready to start the debate. "The Republican Party after . . . World War II was an internationalist party," he said. "We reached out. . . . We developed consensus in the world. That was done through many avenues, associations, coalitions and common interests."

Today, Hagel said, many Republicans question the value of working so closely with those institutions, including the United Nations and NATO. Hagel also said that he fears the protectionist instinct within the party and that it could threaten the Republican commitment to free trade.

Vin Weber, a former House member from Minnesota, dismissed Hagel's concerns about trade. Although the GOP has gone through a series of debates about trade since conservative commentator Patrick J. Buchanan first ran for president in 1992, Weber said, it "has been the party of free trade, it will remain the party of free trade, and I don't think there is a big debate over that."

But on the question of the United States' relationship with the rest of the world -- on when, if ever, the United States should go it alone, on whether international institutions inhibit or enhance U.S. interests abroad -- Weber predicted a coming debate. "I think there is a division between the parties and maybe within the Republican Party," he said.

Even more likely is a debate over fiscal policy and the role of government. Bush has presided over a significant expansion in the size and power of the federal government as he has built up the Defense Department and the new Department of Homeland Security to wage two wars abroad and protect the homeland. But coupled with his tax cuts, the deficit has exploded, and the long-standing tensions between deficit hawks and the tax-cut wing of the party have intensified.

The tax-cut wing occupies a dominant position within the party, a shift over the past two decades from a time when what was known as the "green eyeshade" wing held sway. Republicans have accepted the growth of government under Bush as a necessary cost of dealing with the terrorist attacks of Sept. 11, 2001, but party members predict a big fight over spending and deficits, either in a second Bush term or in Bush's absence.

The party's problems attracting support from minority voters present another challenge that could spark debate. Bush strategists long ago identified the demographic time bomb of the Latinos' surging growth numbers and have said Republicans must improve the party's performance among Hispanics or suffer significant political consequences.

Sen. Lindsey O. Graham (S.C.) describes the party's racial gap in moral terms. Graham said the book "A National Party No More," written by Sen. Zell Miller (D-Ga.), whose biting critique of his party and Kerry produced one of the most riveting moments in New York, could just as easily be about the Republicans, given the GOP's limited support among Latinos and paucity of support among African Americans.

"We're at the height of the Roman Empire for the Republican Party," Graham said, predicting a Bush reelection and expanded majorities in the House and the Senate. "But the tide slowly but surely goes out."

A decade from now, Graham said, the party could be in terrible shape: "If we continue to lose 90 percent of the African American vote -- and I got 7 percent -- if we continue to lose 65 percent of the Hispanic vote, we're toast," he said. "Just look at the electoral map."

Social issues present another concern for the party. Some of the most enthusiastically received speeches in New York were delivered by Republicans at odds with the party on abortion and gay rights, particularly Giuliani and California Gov. Arnold Schwarzenegger.

Some Republicans see this convention as evidence that there may no longer be a social-issue litmus test that prospective presidential and vice presidential nominees must pass. Others, such as Weber, note that conservatives have won the social-issue battles decisively and that, in 2008, the party "is going to nominate a social conservative."

McCain has differed with his party often and opposed Bush's call for a constitutional amendment to bar same-sex marriages, but on abortion and guns, he has a voting record in line with the current Republican orthodoxy.

Giuliani has no such record to point to, but Whit Ayres, a GOP pollster, said Giuliani has the kind of political personality that transcends ideology. "He's got an image that's larger than life almost, which makes him a fascinating potential candidate," he said.

Few dispute that a Bush loss will result in intraparty warfare, but with an open fight for the party's presidential nomination looming in 2008 and no obvious successor, it appears inevitable that the divisions Bush's leadership has bridged or overshadowed will reappear as his presidency reaches its final years.

Sen. Chuck Hagel (Neb.) predicts a period of introspection and debate over the GOP's future. Ralph Reed is among those who believe that a second Bush term will resolve festering party disputes. "If we continue to lose" much of the minority vote, "we're toast," says

Sen. Lindsey O. Graham (S.C.).