This idea of FAs wanting to come here or not is real, but I look at it a little differently. There are going to be some elite FAs (divas I call them) that may turn their nose up at the Pats because they are looking for a win now situation or whatever. For that type of FA, throwing more money at it probably doesn't change anything. But is that the level of FA we should be chasing right now?
We have the coach now (hopefully) and we have a promising young QB now (key word young). We need good players all around, we don't need divas right now. It doesn't make sense for the diva and it doesn't make sense for the Pats to over spend on one position or player. We should be targeting good players to build the infrastructure, start building something, then when we are closer, that is the time to target a specific diva that may put us over the top.
Second tier FA OL (for example) are still going to be way better than what we had last season. We can overpay a little for that type of player, improve the team tremendously, and not break the bank. Still need someone who can evaluate those players, but NE could be a good spot for that type of player. Same on defense, just get a little better everywhere.