With Welker I'm sure there's a number NE would agree to before the season ends but it's likely to be really low (3/12 in new money to make a 4/15 total contract or something in that ballpark). I suspect they don't get a deal like that done and instead let him play out his now ridiculously team-friendly contract and offer him a reasonable contract if he's been healthy and productive.
That sounds much more like what you want them to offer than what the Patriots would actually offer. I can't imagine they would be stupid enough to deliberately lowball him so as to piss him off and encourage him to go FA. Do they want a good deal, of course, are they so stupid they offer a deal worth about half of what he would be willing to sign for? I sure hope not. If they made that offer and i were Welkers agent I would end discussions and let him know the Patriots no longer want his services and to go max out on the open market.
You either think Welker is a ****** or you just hate him as a player as you clearly have no understanding of his value to this team.