I've never been a big fan of mid-season coaching changes - either you knew the guy wasn't doing what you wanted way before the season started, in which case you should have fired him then and done a full search, or you thought he was the right guy and you changed your mind after 20-odd games, which means you don't have a good sense of how to handle small sample sizes.
Washington is #5 in the league this season in possession (as quantified by what we call "Fenwick Close Score" - tied in any period, or within one goal in the first or second period.) They haven't been that good since 2007-08 and 2008-09 (they were 16th last season.) Of course, Washington's 5-on-5 save percentage is 29th in the league (they finished 8th and 2nd the last two seasons), so when a GM sees short-term luck-driven fluctuations like that, he has no choice to fire his coach.
And, of course, save percentage lows like this don't last long, so when Tomas Vokoun's save percentage rebounds to career norms as we expect it to, Washington will start winning a lot and firing the coach will look like a genius move. If you're trying to score genius points with the press, then by all means fire the coach and watch your team regress upwards...But if the focus is long-term winning, firing a coach mid-season makes no sense.