I seemed to recall a previous AG that was held in Contempt of Congress (Eric Holder) The consequences to him were nonexistent. He was involved in "Fast and Furious" operation that wound up getting at least one American killed.
I'm assuming that the similar consequences will apply to AG Barr.
As far as jail time goes, same comment applies. Holder got none for adding and abetting murder so not talking to The house committee is even less serious so nothing should happen.