In my mind, whether or not to fire the coach results in the answers to a few very simple questions:
1. Does the team have better talent than the record shows? The answer to this is simple: yes. The Redskins have enough talent on offense to outscore just about anyone. There are some holes, but there isn't an NFL team without holes. The teams having successful seasons have gameplanned around the holes, and been successful. The defense lacks talent at some positions, and at other positions players are out of scheme, which is on either the coaching staff, or possibly the owner (if Snyder insisted upon the 3-4, which I doubt.)
2. Are there extreme circumstances causing the team to underperform? The Falcons and Packers have struggled with injuries to key players. The Redskins, on the other hand, have been, on the whole, healthier than last year. Yes, there are players missing. But last year, the team reached the playoffs without Orakpo, and also lost Garcon for some time. Helu was also out, and he clearly adds a lot to the offense. No excuse here. The only possible excuse is the cap penalty, which certainly hurt the chances for the team to improve the line.
3. Is the team beating teams it should beat? Almost every team is more talented than another team. They should win that game. The Redskins have faced the Raiders, Cowboys, Vikings, and Eagles (twice). The Eagles and Cowboys are close to identical in terms of talent, the Raiders and Vikings are less so. The Redskins are 1-4 in those games. The Redskins have two games left against the Giants and one each against the Cowboys and Falcons. If the Redskins do not win at least 3, possibly 4, of those games, it is clear the team is (once again) playing to the level of the opposition, which is a clear sign of a coach who is not succeeding at motivating the team.
In regards to Shanahan, he fails at least two of three to this point, and is in his fourth season with the team. Making matters worse, several other teams have gone from doormats to contenders in this time. In 2009, the Seahawks were 5-11 in the worst division in football. The Lions went 2-14, one year after failing to win a game. The 49ers had gone 8-8, but had been consistently bad for years. Two of these teams are now among the premier teams in the league, and the Lions aren't far behind. The Redskins have taken one big step forward, and two giant steps back. Unless the team finishes strong and he demonstrates capable leadership, I see no reason not to fire him at the end of the season.