The league obviously has to be cognizant that not every problem with the Garden ice can be fixed with the wave of a magic wand, so I doubt they'd really pounce on this. Plus, at least the Bruins haven't had to delay a game due to ice problems in recent history...IIRC, Carolina had to schedule a triple-header against Detroit last year because of their ice problems. (I may be totally mixing up the problems, but it happened to someone, somewhere, and there was no better scheduling solution than a triple header including two games with both teams playing B2B in the offending arena.)
What seems to me to be more likely is that the league could more subtly threaten JJ and the crew with removal of perks such as the Winter Classic. As it stands now, from what I understand, we're basically ineligible for events like the Draft and the ASG because we don't have a nearby convention center. But removing those marquee events, and perhaps having the Bruins play in China, might be the main leverage the league has.
That said, the Bruins are, in my uneducated guess, probably one of the bigger national US TV draws, so the Bruins have some leverage too - the league could be shooting themselves in the foot. Our fans are more spread out than, say, Vegas or Arizona. That's not to say that there aren't other easy substitutes - any of the US Original 4 plus Pennsylvania can be a good TV draw...at least that's what I assume, since NBC puts them on TV all the time.