At least according to overthecap.com, if we cut him next year, we still eat $8,000,000 in dead money. So he should be here at least 2 more years even if he is a backup.
True we would eat 8 million in dead money by cutting Byrd in 2017, but his cap hit for that year is 11.7 million. So the Saints would actually gain 3.7 million in cap space by cutting Byrd in 2017.