Surveys there indicate that about half the Democrats planning to participate in the caucuses are moderate or conservative; many of these voters have said they are uncommitted or are supporting Mr. Biden but willing to change their minds.

Some candidates have more maneuvering room than others to challenge the two leaders: Whereas Mr. Buttigieg and Mr. Sanders are flush with cash, Ms. Klobuchar is in a far more tenuous financial position and has yet to qualify for the debate in November. At least a few other candidates who took an assertive approach Tuesday are in similar straits, straining to raise money or meet the debate threshold or both.

What could prove decisive in Iowa, and beyond, is if centrist voters coalesce behind a single candidate or fracture among the group of hopefuls presenting themselves as pragmatists. If Mr. Biden cannot recover a measure of momentum, but holds on to enough support to block other candidates from building a coalition of more moderate Democrats, it could allow Ms. Warren or Mr. Sanders to roll through the earliest primaries and caucuses with relatively weak opposition.

This scenario, of a sort of zombie Biden candidacy, is what most alarms supporters of other center-left Democrats in the race.

Mayor Nan Whaley of Dayton, Ohio, a close ally of Mr. Buttigieg, predicted the South Bend mayor would now “dig down deep in Iowa and New Hampshire,” carrying his message from the debate — a combination of uplifting rhetoric about the future and blunt criticism of certain progressive policies — into the early states where he’s polling in fourth place.

Ms. Whaley said she expected Mr. Buttigieg, 37, to make a determined effort to displace Mr. Biden as the candidate seen as most capable of speaking to Midwesterners.