His speaking style — a hope-and-change Obama impersonation, crossed with the mid-set banter of a brooding singer-songwriter — connected until it did not.

His eagerness to please — feet tapping atop cafe counters, hands slicing the air, head held in a permanent display of attentiveness — began to grate on some Democrats who had preferred such tics when he was merely the alternative to Mr. Cruz, a Republican they loathed.

Another sensation, Mayor Pete Buttigieg, was fresher, younger, quicker on his feet, crowding the not-classically-qualified lane that Mr. O’Rourke once seemed to own.

And after criticism early in his campaign over a dearth of major policy plans, Mr. O’Rourke had, by the end, so tested the bounds of acceptable debate within the party (“Hell yes, we’re going to take your AR-15,” he vowed after the El Paso shooting) that some of his peers had worried that he was hurting the cause.