Impact of paying off children's school debts?

My daughter has over $100 K debt for law school. I realize my wife and I can gift $13 K for both us each year ($26K) to her. If I paid her debts off in total this year, that is beyond the $26 K. I we paid it off , does she have to report it as income, and does the $100K towards the estate exemption for our death? I saw something that paying above the yearly amount would affect our estate exemption.