By rule they are not required to negotiate. One instance is Sean Gilbert, and possibly the precedent...
"The Commanders made Gilbert their franchise player, but rather than sign the one-year $3.4 million tender offer, Gilbert sat out the 1997 season. After the 1997 season the Commanders again made Gilbert a franchise player, this time offering a one-year contract for $2.97 million (the average of the 5 highest paid DTs). Gilbert objected and asked for arbitration saying the Commanders did not have the right to place their franchise player tag on him for a second straight year.
On March 17, 1998, the NFLPA and the NFL had an all-day hearing to resolve the case.
"The Commanders received compensation of two first round draft picks from the Carolina Panthers for not matching the Panthers offer of 46.5 million dollars."
If the agent wants to play hardball, we play.