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 the strength 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.