A little shaky, the camera shows Gov. Chris Christie of New Jersey shedding his sport coat at a town-hall-style meeting as a teacher criticizes what she sees as his attacks on her profession. He begins to respond, the woman tosses her head in frustration, and Mr. Christie goes for the jugular.

“I stood here and very respectfully listened to you; if what you want to do is put on a show and giggle every time I talk, well then I have no interest in answering your question,” he says, as the audience erupts in applause. “If you’d like to conduct a respectful conversation, I’m happy to do it. If you don’t, please go and sit down, and I’ll answer the next question.”

The testy exchange is vintage Christie  or, at least, vintage Christie on YouTube, where it has drawn more than 770,000 views, a number that dwarfs those of his peers around the country and has fueled the buzz about his being a potential national candidate. Since Mr. Christie took office in January, his staff has spread his message on YouTube, posting sharply edited videos of him talking tough or dressing down hostile questioners, a stark contrast with the set pieces that make up most other politicians’ offerings online.

The style and sheer size of the oeuvre  163 videos  has helped make Mr. Christie, a Republican in a largely Democratic state, a YouTube sensation, with myriad fans around the country who can describe his goals, dislikes and manner.