Gov. Ron DeSantis of Florida may have done just enough in the Iowa caucuses on Monday night to argue that he still belongs in the race to defeat Donald J. Trump for the Republican presidential nomination.

But his distant second-place finish had all the feelings of a disaster, given how much time and money he invested in the state, and it calls into question his ability to stay in the nominating contest, with his campaign cash running low and tough tests ahead in New Hampshire and South Carolina.

Mr. DeSantis, who entered the field as one of its most compelling contenders, just barely managed to hold off a late surge from Nikki Haley, the former South Carolina governor.

Mr. Trump defeated both candidates so soundly on Monday night that the race was called in his favor by The Associated Press just 31 minutes after the caucuses got underway. The early call — while some Iowans were still caucusing — gave Mr. DeSantis’s team a lifeline to blame the news media for a disappointing performance.