Today, February 20th, is the first day that NFL teams can start placing the franchise tags on their players. Each team has one franchise tag that they can use for the 2012 season. Football Outsiders has a good breakdown of the anticipated cap numbers for offensive players here and defensive players here. Teams have until March 5th to franchise a player.
It is pretty clear that they do not plan to go down that road with Finny. His number would be somewhere around $10 million. That would be about 1/3 of the cap space they have available for 2012.
It is unlikely they use it on Griffin unless Jerry Gray really thinks he can get Griff back to his Pro Bowl level. There is no doubt the ability is there, but something just has not clicked yet. Both parties would probably benefit from a chance of scenery.
There probably won't be a lot of guys who are franchised until closer to the deadline, but there will probably be some big names that end up on the list. The two biggest names that are likely to get the tag are Drew Brees in New Orleans and Ray Rice in Baltimore.