Samuel and his agent are taking the mature approach to the situation likely based on an understanding with the team that one of two things will happen. Either they will continue to productively negotiate to persue a long term deal OR he will be traded to a team who will agree to give him one.
In Briggs case apparently the Bears have indicated to him either directly or implicitly that they are not interested in further negotiations persuant to a long term deal nor do they have any interest in trading the player to someone who is willing to give him his deal.
Each players "attitude" could change over night should their positions become reversed.
Asante is currently keeping the atmosphere light. But so did Deion at this juncture. Difference here is Asante's agent appears to be far more rational than Deion's was and is said to have a good relationship with the team. Asante is skipping the off season program, as he did last year although the circumstances then were his wife was expecting, but claiming the rationale is just that he (now) prefers to workout at home. (A rationale BB does not embrace btw and will likely strucure to avoid if a long term deal is signed.) The next gut check will be mini camp in May (if he is not in fact still shopped or traded pre draft or the team drafts a CB in the first round).
Teams only have until July 15th to work out a long term deal with a franchise tagged player. After that he can only be signed to a one year deal (essentially the tag) until the last week of the season. I believe recently some tagged players have opted to sign an alternate one year deal as opposed to signing their tag that stipulates they will not be re-tagged as a trade off/compromise to get them into camp. Seattle did that with Shaun Alexander.