DES MOINES — As Elizabeth Warren and Amy Klobuchar escalated their attacks on Pete Buttigieg in Thursday night’s Democratic debate, and Mr. Buttigieg forcefully pushed back, a crucial if unspoken fact was driving the political combat: All three candidates are trying to knock each other out in the Iowa caucuses, where they need strong finishes to stay viable in the 2020 race.

Unlike Joe Biden and Bernie Sanders, who don’t need to win Iowa to springboard to the next primary contests, Mr. Buttigieg and Ms. Klobuchar have virtually no path to the nomination without exceeding expectations in Iowa with a victory or at minimum a top-three result. Ms. Warren, who has fallen out of first place in Iowa polls but has a strong organization there, is looking for a momentum-reviving rebound — or at least a way to halt Mr. Buttigieg’s rise there.

Rarely are presidential primary debates as clarifying about the political stakes for candidates as Thursday’s Democratic face-off, where Mr. Biden largely held back and Mr. Sanders trained most of his fire at the former vice president — both content to let the other three candidates duel and perhaps diminish one another with attacks over experience, fund-raising, free college and “wine caves.”

“Warren has to win Iowa, Pete has to win Iowa, Amy has to pull as close to the top as possible to leverage her way into the top tier,” said David Axelrod, the longtime political strategist who helped Barack Obama win the Iowa caucuses in 2008 and build momentum against Hillary Clinton in their long nomination fight.