“Free every Dreamer of any fear of deportation by making them American citizens now,” Mr. O’Rourke proclaimed, responding to a question about the children of immigrants who are known as Dreamers that came from a Hispanic woman who said she herself was one of them.

A middle-school-age boy said he wanted to know what could be done to make him feel safer in his classroom. Mr. O’Rourke called for ending the sale of weapons designed “for the express purpose of killing people.”

If they are boilerplate liberal messages, the messenger was received as something special, particularly in Charleston, where Mr. O’Rourke, at the town hall-style meeting at a local high school and a Friday night event at an area brewpub, drew largely white and well-heeled crowds bursting with excitement.

Here and elsewhere, Mr. O’Rourke delivered his message with a rat-a-tat urgency, his knees bouncing in rhythm with his words, with one hand grasping a microphone and the other one gesticulating like a bull rider out of the chute.

Frankie Galizia, 27, a human resources manager from Hilton Head Island, S.C., said he was sold on Mr. O’Rourke because of his “relatable” style and because he hoped he would do a better job on issues he cares about, like L.G.B.T. rights.

He wanted to know as much as possible about the Mueller report’s contents, he said. But for now, it “takes a complete back seat to the major issues this country faces.”

The situation was much the same in Concord, N.H., where John Hickenlooper, the former Colorado governor, was meeting with voters.