Of all the Democratic presidential candidates still in the race, it has been Ms. Klobuchar, the Minnesota senator, and Mr. Buttigieg, the mayor of South Bend, Ind., who have worked hardest and deepest to win over Iowa’s more moderate Democrats, pitching themselves as Midwestern pragmatists who know how to prevail in red states. Both candidates know they have virtually no path to the nomination without a strong finish in Iowa, and in the six weeks that remain before the Iowa caucuses, it’s likely their competition will only intensify.

Both Ms. Klobuchar and Mr. Buttigieg offer messages about restoring unity in America. They speak about their ability to engage independents and Republicans. At campaign events, many attendees say both candidates are in their top tier.

Yet if Ms. Klobuchar and Mr. Buttigieg have become the race’s most talked-about moderate alternatives to former Vice President Joseph R. Biden Jr., the last weekend before Christmas was also a pointed study in the meaning of momentum. The race is still fluid in Iowa, but Ms. Klobuchar remains in a distant fifth place, behind the top four candidates: Mr. Buttigieg, Mr. Biden, and Senators Bernie Sanders and Elizabeth Warren.

After an unusually spirited debate in which she took on Mr. Buttigieg directly, Ms. Klobuchar tried to capitalize on the fresh interest in her campaign with a 27-county bus tour. On Saturday, her events were energy-filled if still intimate, her crowds growing but nowhere near the hundreds that some top-tier candidates can draw to their town halls and rallies: Dozens of Iowans packed into a coffee shop in Creston for Ms. Klobuchar. They crowded into a back room in Osceola and sat with her at a local restaurant in Corning.

But when a prominent endorser asked the audience in Osceola who had committed to caucus for Ms. Klobuchar, almost no one raised their hands.