No problem. I'll let someone who knows more about the cap answer that, but my guess is that they would be hard pressed to franchise anyone considering their current cap situation. Graham would only be franchised because you simply can't let a guy like that walk away. But I doubt that they'll feel the same way about anyone else.
The non-exclusive franchise tag, cost another team two number one drafts picks to sign the player, for tight ends was $6.066 million last year. Teams are allowed one franchise or transition tag, although the transition is almost obsolete. Teams must designate the tag between February 17-March 3.
The salary goes right on the teams salary cap but they do not need to be under their adjusted cap number, includes carryover about $625,000 in the Saints case, until March 11.
The team can lower the tag number if they can agree to a long term deal with the franchised player by June 15 otherwise the player/team is stuck under the franchise one year salary. The team does have to carry the full amount, about $6 million, on their salary cap and be under the cap March 11 onwards unless they are able to lower it via a long term deal. This does effect the team's ability to sign free agents since the free agency period also starts March 11.
Only the top 51 salaried players and any dead money count on a team's cap as of March 11 instead of 53 and no practice squad salary counts as well, this saves about $1.8 million during the offseason.
There is no way Graham hits free agency the Saints will try and lock him up long term before using the tag, if not they are definitely using it on him, they will find the space. As far as any other Saints free agents only a kicker/punter would be less to franchise then a tight end so it would limit the Saints resources more even if the tag were open for use on another position if Graham was already locked up.