UPDATE: GM Jerry Angelo has confirmed that the Bears will not be using the franchise tag on WR Bernard Berrian.
While I still haven't seen anything stating how Berrian feels about the revised contract the Bears offered him it is thought that the Bears will not use the franchise tag on him if he does not take the deal. They are not interested in getting into another dispute with agent Drew Rosenhaus.
If Berrian signs elsewhere, barring free agency and draft moves their depth chart at wide receiver would be Devin Hester, Mark Bradley, Rashied DAvis, Mike Hass and Brandon Ridaeu.
A source close to the situation with Lance Briggs has said that the revised offer the Bears have made still falls short of what Briggs and Rosenhaus are looking for. With teams such as San Francisco, Washington, Buffalo, New Orleans and Denver interested I wouldn't expect them to just settle. If Angelo wants to keep Briggs, he needs to step up the offer.