The Sanders campaign is arguing that a victory here by Mr. Sanders is not a certainty.

“Now we have a two-way race, one-on-one, and it is going to be played out here in New Hampshire,” said Tad Devine a senior strategist for the Sanders campaign. “That’s our big test right now,” he added. “We have to demonstrate that he can take on Hillary Clinton and defeat her.”

Mr. Sanders vowed on Tuesday afternoon to campaign hard across New Hampshire and said that as in Iowa, his campaign would focus on getting supporters to the polls on election night. “Secretary Clinton won here in 2008,” he told a group of reporters in Keene after a rally. “Secretary Clinton has a very formidable political organization and, as you know, has virtually the entire political establishment on her side. So, you know, we are taking nothing for granted.”

For the Clintons, the New Hampshire primary holds an emotional attachment. It is the state that made Mr. Clinton the “Comeback Kid” after he overcame scandal to place second here in 1992. Mrs. Clinton said she “found my own voice” in New Hampshire in 2008 with a surprise victory here after finishing third in Iowa.

Advisers have encouraged the Clintons to devote more time on Nevada and South Carolina but have been met with resistance because the couple refuse to entertain the idea that what could be the last presidential campaign of their political careers would include a loss here.Mrs. Clinton did not alter her stump speech on Tuesday, but she did turn the focus to a broiling debate inside the Democratic Party, one that pits her more moderate but achievable goals against the liberal ambitions of the big government vision of Mr. Sanders. Clinton advisers said there were no plans for Mrs. Clinton to turn sharply negative against Mr. Sanders, but rather she planned to focus on courting young voters and liberals, the two parts of the electorate that overwhelmingly favored Mr. Sanders in Iowa. New Hampshire polls have shown that many young Democrats here are deeply skeptical of Mrs. Clinton’s honesty and view her unfavorably.

Both candidates are expected to focus intensely on New Hampshire, with Clinton advisers saying that Mrs. Clinton may leave the state only for potential fund-raising events. Mr. Devine, Mr. Sanders’s strategist, said Mr. Sanders might spend a night at home in Burlington, and next week could dip into Massachusetts, which has an election on March 1.