Judas did feel great shame and guilt in his betrayal, attempting to return his blood money, and hanging himself until dead.

I doubt Pence feels guilt, but like Judas, this is going to bite him in the ass, hard. He's a political pariah, and a member of a party who's influence is rapidly going to recede.

Maybe he should release a tell-all book while he still has a chance to build a bit of wealth before he's locked out of prominence forever.