Advisers to Hillary Clinton , including former President Bill Clinton, believe that her campaign made serious miscalculations by forgoing early attacks on Senator Bernie Sanders of Vermont and failing to undercut his archliberal message before it grew into a political movement that has now put him within striking distance of beating her in Iowa and New Hampshire.

According to Democrats close to the Clintons and involved with her campaign, Mrs. Clinton and the former president are also unnerved by the possibility that Mr. Sanders will foment a large wave of first-time voters and liberals that will derail her in Iowa, not unlike Barack Obama’s success in 2008, which consigned Mrs. Clinton to a third-place finish. They have asked her advisers about thestrength of the campaign‘s data modeling and turnout assumptions in Iowa, given that her 2008 campaign‘s predictions were so inaccurate.

As the Democratic rivals prepare for what is likely to be a contentious televised debate on Sunday night, the Clintons are particularly concerned that her «rational message,» in the words of an aide, is not a fit with a restless Democratic primary electorate. Allies and advisers of the Clintons say Mr. Sanders is clearly connecting with voters through his emotional, inspiring rallying cry that the American economic and political systems are rigged for the wealthy and powerful. By contrast, Mrs. Clinton has laid out an ambitious policy agenda, but more recently has been stressing her electability and questioning the costs of Mr. Sanders‘s ideas.

Most Clinton advisers and allies would speak only on the condition of anonymity to candidly assess her vulnerabilities and the Clintons’ outlook on the race. This article is based on interviews with 11 people — campaign advisers, outside allies, friends and donors — who have spoken to the Clintons about the race.

«Hillary is a pragmatic progressive — she’s not an advocate,» said Gov. Peter Shumlin of Vermont, who last week campaigned in Iowa for Mrs. Clinton over his home-state senator Mr. Sanders. «She quietly pulls people together and gets things done. Even though that’s not in vogue right now, I think that’s what voters will want in the end.»

But Mrs. Clinton‘s problems are broader than just her message: Opinion polls show that some Democrats and other voters continue to question her trustworthiness and whether she cares about their problems. Recent polls show that her once-formidable lead over Mr.Sanders in Iowa has all but vanished , while he is holding on to a slight lead over her in New Hampshire .

Mrs. Clinton and her team say they always anticipated the race would tighten, with campaign manager Robby Mook telling colleagues last spring that Mr. Sanders would be tough competition. Yet they were not prepared for Mr. Sanders to become so popular with young people and independents, especially women, whom Mrs. Clinton views as a key part of her base.

Given her many political advantages, like rich donors and widespread support from Democratic Party elites, she is also surprised that Mr. Sanders‘s fund-raising has rivaled hers and that her experience — along with her potential to make history as the first woman elected president — has not galvanized more voters.

«It was probably never going be a straight line — we hoped it would be but feared it wouldn’t be,» said James Carville, the Democratic strategist on Mr. Clinton‘s 1992 campaign and a longtime friend of the Clintons. «She’s performed solidly enough, but it’s been a hard race.»

Several Clinton advisers are also regretting that they did not push for more debates, where Mrs. Clinton excels, to more skillfully marginalize Mr. Sanders over his Senate votes in support of the gun industry and the enormous costs and likely tax increases tied to his big-government agenda.

Instead, Mrs. Clinton, who entered the race as the prohibitive favorite, played it safe, opting for as few debates as possible, which were scheduled at times when viewership was likely to be low — like this Sunday at 9 p.m. on a long holiday weekend.

«In the debates, she has shined, and while conventional wisdom says they offer no upside to a front-runner, she would benefit from more,» said Carter Eskew, a Democratic strategist who was a senior adviser to Al Gore’s presidential campaign in 2000. (He is not aClinton adviser.) «Her basic strength remains: She is strongest in comparison to others. Her seasoning and knowledge show best in contrast.»

Several Democratic leaders agreed, saying the Clinton campaign underestimated Mr. Sanders from the start. They argued that Mrs.Clinton and her advisers should have competed against him more aggressively, in debates and on the campaign trail, rather than appear so sharply negative with their recent attacks, which have given the campaign a jumbled feeling heading into the first voting states. Even Chelsea Clinton jabbed at Mr. Sanders , an unusual move given that relatives are traditionally used in campaigns to soften a politician’s image.

«I always say, ‘If I’ve got an opponent that’s breathing, I’m going to take that opponent very seriously,’ » said Representative James E. Clyburn of South Carolina, who was expecting to host Mrs. Clinton and Mr. Sanders on Saturday night at his famed fish fry. Mr. Clyburn, who is not endorsing a candidate before his state’s primary, said Clinton aides in South Carolina had expressed misgivings to him about the state of her campaign.

«It has to do with what things ought to be done and when they ought to be done,» Mr. Clyburn said, declining to provide more details. «The reality is, if Mrs. Clinton loses Iowa and New Hampshire, that could create new and real problems for her here.»

Some Democrats also believe Mrs. Clinton may have benefited from a more competitive primary season with big-name rivals, like Vice President Joseph R. Biden, Jr., who might have brought out the fighter in her. Only this month has she started to engage Mr. Sanders , and some of her jabs have looked sudden and anxious.

«If the vice president had run, I still think Secretary Clinton would be on course for the nomination, but I also think he would have put her through paces that would have made her even stronger for the general election,» said Bill Burton, a former adviser to President Obama. «It also would have given her the kind of fight in which she thrives.»

Both Mrs. Clinton and her husband believe she can still win the Feb. 1 caucuses in Iowa and the Feb. 9 primary in New Hampshire despite Mr. Sanders‘s gaining ground recently and now being virtually tied with her in many polls in those states. But the Clintons also believe she can survive losses in both places because of the strength of her political organization and support in the Feb. 27 primary in South Carolina and in many March 1 Super Tuesday states and other big states to follow.

The Clintons have long thought that the state-by-state demographics of the primary electorate would matter far more than the political momentum that Iowa and New Hampshire victories can provide, and that the large numbers of blacks, Hispanics and moderate Democrats would benefit Mrs. Clinton more than Mr. Sanders in the South and in other March and April primaries.

Jennifer Palmieri, the Clinton campaign‘s communications director, expressed confidence that Mrs. Clinton would prevail in the long run.

«We have always known that this race would be hard fought,» Ms. Palmieri said in an email. «Democratic primaries always are.»

«That’s why Hillary Clinton has worked so hard to both build a strong grass-roots organization, and make her case to voters as to why she is best choice to lead the party as the Democratic nominee and serve as president,» she added.

Yet some Democratic Party officials who remain uncommitted said that after nine months of running, Mrs. Clinton still had not found her voice when it came to inspiring people and making herself broadly likable. While Mrs. Clinton is known for connecting well with people in small settings, she has not shown the same winning touch as consistently at rallies or in television interviews, they said.

«Hillary struggles to convey sincere passion with issues that matter to the general public, unlike Bernie Sanders and Elizabeth Warren,» the Democratic senator from Massachusetts, said Lawrence Taylor, a superdelegate from Oregon. She does so best in the televised debates, said Mr. Taylor, who believes those forums have made her «stronger» and helped her come across as more trustworthy.

Another uncommitted superdelegate, David McDonald of Washington, said that compared with eight years ago, Mrs. Clinton was less prone to stumbling and had a better political operation in his state. But just like in 2008, when she faced an opponent, Mr. Obama, who could mesmerize crowds, Mrs. Clinton risks being overtaken.

«Her voter base does not seem as gung-ho energetic as Sanders‘s base,» Mr. McDonald said. «It may be that they feel like they are waiting for the real race to begin. But an enthusiastic base can make a big difference in the early stages of a presidential nominationcampaign, and if Hillary can’t pull away from Sanders fairly early in the season, I suspect he will gain strength rapidly.»

Clinton Campaign Underestimated Sanders Strengths, Allies Say