Bruins don't win the Cup this year and all the Fire Sweeney people will be back.
If they don't win this year it will either be on the players, bad luck, or the simple fact that things can happen in a seven game NHL playoff series when two good teams play. (Especially when random goalies can get insanely hot at the right time and steal a series.) If they don't win it will NOT be on Sweeney. He has put them in as good a spot as humanly possible. There's zero denying he's done an amazing job this year.
If they come up short the fair criticism in regards to him will not have anything to do with the job he did this year, but that he didn't make these kinds of moves in previous seasons to expand their championship window. Depending on what Bergeron and Krejci decide to do this could sort of be a "this is our only real shot for the foreseeable future" type go. And like I just said, one playoff series can ruin everything. Look at Tampa getting swept in Round 1 the year before they won 2 straight Cups and went to a third Final. Shit happens in a short series, which is why you want as long a chance as possible to win.
How many years did we beg for him to fill the hole in the top 6? Or to get another defenseman who could carry a big load? And every year he didn't and those weaknesses manifested in the post-season. Those were fair criticisms then, and the fact he's making big moves this year proves they were. He CAN make big NHL trades that fix the roster. Better late than never, obviously, but it doesn't change the past. (On the flip side, the past is gone and done and it's time to enjoy the upcoming spring and hopefully June.)
I wish we got this Sweeney five years ago. But people can get better at their job and he CLEARLY has based on his performance this season alone. He's like a totally different GM all of a sudden. This is a guy last year who traded a second for cap space and then didn't use it!
All of which is a long way to address your original point: even if they get swept in Round 1 this year I will not call for him to be fired again.* Failure to win a Cup or even seriously contend for one this year won't be on him the way it was in previous seasons. A+ job by him.
*I will never forgive him or Neely for the Mitch Miller bullshit. I think they're bad humans, but I'm talking about Don Sweeney the GM in this post.