The logistical anarchy of Monday evening has already accelerated calls to strip Iowa of its privileged status as the first stop for prospective presidents. The state’s top Republicans, including Gov. Kim Reynolds, issued a statement on Tuesday defending Iowa’s nominating perch, and Mr. Trump said he would protect the tradition as long as he is president.

But as the state’s caucus-counters and national Democratic leaders slogged through a bleary, clarity-free Tuesday morning, the most pervasive emotion may have been defeatism. The angst multiplied for progressives with news that Michael R. Bloomberg, the billionaire former New York mayor, plans to escalate an already ubiquitous advertising campaign for his presidential bid.

Some moderates immediately argued that the messiness of Iowa has only validated Mr. Bloomberg’s bet on bypassing the early states to focus on contests in March and beyond. And Republicans suggested that the mishap should disqualify the rival party from executive governance altogether.

“Dems right now can’t even stand in a gymnasium and count how many people move under each sign,” Senator Ted Cruz, the 2016 winner of the state’s Republican caucuses, tweeted on Tuesday. “These are the people who want to be put in charge of our health care & everything else in our lives?”

Straining for analogies, political minds on Tuesday invoked an episode from Mr. Cruz’s days as a young lawyer on George W. Bush’s 2000 presidential campaign: the Florida recount and its attendant mayhem.

Was the “coding issue” bedeviling Iowa Democrats the new “hanging chad”? Could the Supreme Court be summoned to sort out the holdup?

Some veterans of the Florida affair wondered if the comparison might be unfair. To Florida.

“What’s happening out there makes the recount look quite orderly and structured,” said Mac Stipanovich, a longtime strategist and lobbyist who played a pivotal role in 2000 advising Katherine Harris, Florida’s Republican secretary of state at the time.