The "first vice lady" is either the best at vice, or a heartbeat away from becoming a lady.
The "vice first lady" is a heartbeat away from replacing the president's wife, or possibly the lady figurehead of a campaign to put vice at the top of the agenda.
These are far more interesting than "second lady" but sadly it seems like that is the clear choice as an extension of the concept of "first lady". If Michelle Obama is foremost among ladies, Jill Biden is the runner-up, or second lady.
Incidentally, thinking about what the husband of a female president might be called highlights just how old-fashioned the thinking behind this term is. It's unlikely to become an issue for a while, though, since if Bill Clinton ends up in that position he would in any case still be "President Clinton".