Senator Clinton’s advisers contend that new poll numbers should put to rest doubts about her electability, though some analysts say the numbers, which show her with large leads over the Democratic presidential pack in key states, are far from conclusive.

In Iowa, Mrs. Clinton led a former North Carolina senator, John Edwards, 35% to 18% among likely caucus-goers in an American Research Group poll. In New Hampshire, Mrs. Clinton’s nearest opponent was Senator Obama of Illinois, whom she led 39% to 19%.

In states where politics is less of a public obsession, Mrs. Clinton seems to have even stronger support. A Detroit Free Press-Local 4 survey had the former first lady with 49% among those expecting to vote in the Michigan Democratic primary, well ahead of Mr. Obama, who came in second with 20%.

“Can Hillary Clinton win? Poll after poll make pretty clear that she already is winning,” a spokesman for Mrs. Clinton, Howard Wolfson, said.

A professor of politics at the University of Virginia, Larry Sabato, said Mrs. Clinton’s rise in the polls will be short-lived and has been driven by publicity surrounding the recent kickoff of her campaign.

“That’s a very temporary reaction,” Mr. Sabato said. “We’ll be back to the status quo within a month or two.”

While most of the numbers focus on who has a leg up in states that hold early primaries, some polls showed Mrs. Clinton with a lead of a few points over the top Republican candidates, Mayor Giuliani and Senator McCain of Arizona.

Mrs. Clinton’s camp hopes numbers like those can undermine concerns about her electability, which may be the main obstacle she faces in her bid for the Democratic nomination. In July, more than six months before Mrs. Clinton launched her presidential exploratory committee, two of her top advisers wrote an unusual op-ed piece for the Washington Post, dismissing the talk in Washington and elsewhere that the New York senator could not win the general election. A political strategist, James Carville, and one of Mrs. Clinton’s pollsters, Mark Penn, tried to debunk that notion, but they also signaled their concern that such a perception was taking root.

Despite the poll numbers, quotations and entire articles highlighting doubts about Mrs. Clinton’s electability keep appearing. At least one of her Democratic opponents, Senator Biden of Delaware, publicly stoked the doubts last week by saying the former first lady “is known by 100% of the people” but can’t get above 40% in polls. Many voters say that while they personally like Mrs. Clinton and agree with her views, they doubt their neighbors can be persuaded to vote for her.

A political scientist at the University of Texas, Daron Shaw, said past academic studies have focused on how voters changed their preferences based on earlier states’ primaries or caucuses, but the 2008 calendar is so compressed that the pivotal signals about whether Mrs. Clinton is electable will come from polls and pundits. “Her fate could be known in advance of her actually contesting a primary or a caucus,” Mr. Shaw said. “If Obama’s star rises and falls by next October and she’s sailing along at 45%, it could be done. She could be seen as being inevitable.”

Mr. Obama also faces electability issues, based on his meager experience and on lingering questions about whether Americans are ready for a black president.

Mr. Shaw said he thinks concerns about Mrs. Clinton’s electability are overrated and that her Democratic and Republican opponents may find it hard to build opposition to her, beyond the 40% of people who already disapprove. “I don’t know how easy that is,” he said. “She is somebody who’s already been through the kind of bruising trial by fire.”

Some argue that Democrats should take a lesson from 2004, when second-guessing about who was electable led many voters to back Senator Kerry of Massachusetts, even though they did not consider him their first choice. “Will talking about electability actually lead the Democrats to nominate a candidate who is, in fact, electable? Recent experience suggests it may not,” Jonathan Cohn wrote on the Web site of the New Republic last month.

Yet Mr. Sabato said it can be pointless to vote without some kind of an eye on electability. “It’s really the people who consider electability who save the hides of the party,” he said.

A political science professor at the University of California at San Diego, Gary Cox, said the notion of strategic voting dates back to the 19th century and has even spawned claims that it is immoral or unethical to vote for anyone other than one’s first-choice candidate. “That complaint has also been around since the 19th century,” Mr. Cox said. “The retort that it’s not necessarily dishonest or morally offensive has also been around. I’m not aware that there’s been particular progress on that debate,” he said with a laugh.

One way to allow voters to vote with both their heads and their hearts is through instant runoff voting, a ranked-choice method in use in San Francisco and being phased in by other localities around the country. The Iowa caucuses, which will serve as one of the first real-world tests for the 2008 presidential candidates, have a similar feature under which voters declare their favorite candidate at the beginning of the evening but are gradually diverted to other choices if their first-choice candidate doesn’t get a minimal level of support.

In a separate development, Mr. Giuliani edged closer to formally launching his presidential bid yesterday. He converted his political effort from a testing-the-waters group to the exploratory committee structure favored by most other candidates.