It was a moment that crystallized Senator Hillary Rodham Clinton’s struggles in Tuesday night’s debate. Questioned about a plan to grant driver’s licenses to illegal immigrants, Mrs. Clinton at first seemed to defend it, then suggested she was against it, until finally, pressed for a direct answer, she accused the moderator, Tim Russert, of playing “gotcha.”

Her verbal twists and turns provided her opponents with fodder for their central critique of Mrs. Clinton, which coursed throughout Tuesday’s debate: that she was trying to have it both ways on the issue, much as she was trying to portray herself as antiwar while voting to authorize the use of force in Iraq.

Like the debate over Iraq, the exchanges over granting licenses to illegal immigrants underscored the tensions for Mrs. Clinton as she seeks to court various interest groups who are the building blocks of winning the Democratic nomination.

She has recently intensified her efforts to win the caucuses in Iowa, where an influx of illegal immigrants has raised concerns among many of the state’s long-term residents. But she must also court Hispanic voters who are expected to wield greater clout this election season through early primaries in New York and California.

Mrs. Clinton’s struggles over the issue reflect the hesitancy earlier in the presidential campaign over the Senate compromise immigration legislation last spring, where she had not taken a stand as recently as a week before it was voted on. While there is broad agreement in both political parties about the need for tighter border security, the thorniest issues in the immigration debate center on how to handle the more than 12 million people who are already living illegally in the United States.

Since the failure of immigration overhaul in Washington last spring, the path to citizenship supported by many Democrats has been blocked. With no resolution in sight, the burden has fallen to state and local governments, and their struggle, reflected in the driver’s license proposal by Gov. Eliot Spitzer of New York, is forcing leading presidential contenders to state specific positions.

“The Democrats clearly do not want to antagonize Hispanic voters,” said Muzaffar Chishti of the Migration Policy Institute’s office at the New York University law school. “They are very important in swing states. At the same time, there are many Democrats, especially in the labor unions, who are not as liberal in immigration policies.”

Mrs. Clinton’s campaign, moving rapidly to blunt criticism of her debate performance, sought to clarify her remarks on Wednesday, as she offered general support for Mr. Spitzer’s revised proposal, which would create a three-tier system that would provide government-issued identification for illegal immigrants so they could legally drive.

Two of Mrs. Clinton’s opponents, Senator Barack Obama and John Edwards, support granting licenses to illegal immigrants, although Mr. Edwards has problems with elements of Mr. Spitzer’s proposal.

During the debate, Mr. Edwards accused Mrs. Clinton of saying “two different things in the course of about two minutes.” On Wednesday, Mr. Obama told The Associated Press that her debate performance “left us wondering where she stood on every single hard question from Iran to Social Security to drivers’ licenses for undocumented workers.”

“This may be smart politics by Washington standards,” Mr. Obama added, “but it’s not what America needs right now.”

Until Tuesday’s debate, Mrs. Clinton had not had to confront the immigration issue so starkly. Her adopted state of New York has a long history of dealing with immigration issues, and Mrs. Clinton has heavily courted the immigrant groups that are central to its population mix.

Now she finds herself on different terrain, campaigning in important early primary states like Iowa and South Carolina where candidates are routinely pressed for their views on immigration from an electorate often agitated over illegal immigrants.

Illustrating the political dangers of the issue, Mrs. Clinton found herself under fierce attack Wednesday from Republicans and conservative radio hosts for her debate comments.

“I know there are some politicians like Hillary,” Rudolph W. Giuliani told the conservative talk radio host Glenn Beck. “They say different things to different people. They use different accents in different parts of the country. I’m used to that about her now. I had never seen it happen all in one place, in one minute.”

Mr. Giuliani, the former New York City mayor and formerly a champion of the rights of illegal immigrants, had himself previously defended an executive order that instructed city agencies not to ask the immigration status of any person.

Mrs. Clinton’s aides said her statement Wednesday expressing general support for Mr. Spitzer’s plan was intended to signal that she broadly supported his goal of granting driver’s licenses to illegal immigrants. But they said she had not studied — and was not endorsing — any specific plan.

Mr. Spitzer initially proposed a blanket program of giving full-fledged driver’s licenses to illegal immigrants. In the face of sharp opposition from state lawmakers, he backed off and presented the tiered system.

In issuing the statement, Mrs. Clinton was trying to deal with the concern that she was not taking clear positions on issues. Still, the wording of the statement was murkier than what many of her opponents have said in either supporting or opposing Mr. Spitzer’s initiatives.

After the debate, Mrs. Clinton did not again publicly address the issue herself, but her campaign struck back at Mr. Obama by mocking his theme of “the politics of hope.”

“With each attack, Senator Obama undermines the central premise of his candidacy,” said Mark Daley, a spokesman for the Clinton campaign. “The politics of hope that once characterized his remarks has now been replaced by the kinds of jabs one typically sees from candidates desperate to gain traction in the polls.”

Making the matter even stickier, many opponents of driver’s licenses for illegal immigrants have seized on the possible national security implications.

Mrs. Clinton must contend with the implications of her positioning among more than just caucus-goers in Iowa. Unions, traditionally key Democratic Party supporters, are split over the issue, with many angry at proposals to create guest worker programs that they see as undermining American workers.

Mr. Chishti, the immigration expert, said Hispanic voters, between the 2004 and 2006 elections, turned to Democrats in greater numbers than any other voting block.“They do not want to risk losing that support,” he said.

In the Senate compromise legislation last spring, Mrs. Clinton tried to push through an amendment to make it easier for legal immigrants to bring family members into the country, but she ultimately voted for the bill. Mr. Obama and Mr. Edwards also had not taken a public position on the measure before the vote.