The Bills put the franchise tag on the 26-year-old after failing to come to an agreement on a contract earlier in the year.
However, the safety has now boycotted the team's training camp and a new deal looks a long way from being agreed.
Brandon told The AP: "Obviously, our goal was to have that done by July 15. We didn't meet that goal.
"But we'll pull up our boot straps, and as soon as we can start on that again, we will."
Byrd was drafted 42nd overall by the Bills in the 2009 draft.