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.