The Penguins' mid season coaching change is often referred to in these discussions. But I don't see firing Mike Johnston, who had no NHL experience or success, and firing Claude Julien, as being all that similar. And whoever comes in is certainly not going to have the loaded roster Mike Sullivan inherited.
Someone compared the Bruins to the Vikings in one of these threads. Here's another - the Texans from a couple of years ago. Fans were reactionary in calling for the head of coach Gary Kubiak, when the real problem was at QB.
Well two years after being fired, Kubiak won the Superbowl; the Texans' QB situation still hasn't been properly addressed (though they tried), and the team is still stuck in the mud.
So firing Julien may or may not be the right thing to do. A change could be beneficial to both sides. But until the real problems are addressed, any coaching change will likely have minimal effect.