They can't sign him for less until the Caps, don't qualify him by the due date(not sure what day that is). If he's not qualified, then he becomes a UFA, but then AB can sign with any team. I think as a UFA other teams will give him more than the Caps are willing to give him.
When you qualify a RFA, that means they will get their previous annual amount plus a 8.3% increase at the minimum. So AB's qualified minimum would be around $3.25 million.
I just don't see him being signed by the Caps. Either he's packaged in a trade for a draft pick or he will be, not qualified and sign with another team.
Even if both Hagelin and Connolly walk, I don't think it would be in the Caps best interest to continue keeping AB on the team. He really needs to start fresh with another team.