It's "impasse," for future reference.
Anyway, I think it's a shrewd tactic by the New England camp, if only because it could very well allow Branch to see that no one is going to be willing to pay him what he wants, in turn causing him to accept the Pats' offer. Alternatively, Branch could find a team that will pay him what he wants, and the Patriots might be able to work out a trade and get rid of a headache. The worst case scenario (if a team is willing to meet Branch's contract demands, but is unwilling to give new England anything of value) leaves the Pats exactly where are now - with a disgruntled holdout who they can franchise after the season.
It's a no-lose decision.