Yes, you can get someone cited for contempt of court after failing to appear for a deposition, after you first file a motion in court to compel attendance and the court orders an appearance on a date certain, then the deponent again fails to appear. In CA the penalty is usually 5 days jail time. But it can increase if the conduct continues afterwards.
I have no idea what Jones is thinking here, except that since he didn't produce documents in the other suit which caused him to lose the case by default, and he doesn't want to be deposed in this one, he is clearly hiding things. Why doesn't he just settle the case? Maybe he doesn't have the money to do so.
These plaintiffs will be chasing him around to enforce these judgments against him for years to come. They'll be attaching his bank accounts, liening his properties, and garnishing his wages for a long time. He's probably best off just going BK right now, him and Infowars as both have been sued.
My guess as to what he's hiding is documents which indicate that he never believed Sandy Hook was fake. The one thing he cannot tolerate is his fans finding out that he's been conning them for these past 20 years.