I believe the timing of Amorim’s arrival isn’t bad, the transfer window is just around the corner and he w already had the opportunity to be able to assess the squad and identify the necessary changes to strengthen the team. Amorim’s arrival at mid season allowed him to observe the players performance in competitive matches and make him to gradually implement his tactical philosophy. This period gave him time to analyze the club's strength and weakness, laying a solid foundation for long term success at the club.
The problem is you can't sign many players during the January transfer window. You can only sign 2 or 3 players and 3 players alone won't solve the problem at Manchester United because the 3 players won't be top-class players. Not many top-class players leave their club mid-season for another one and not many clubs release their top players mid-season except you have a very good deal for the club and player which will make you pay more than you're supposed to.
Also, the series of losses and how low they are on the table might have eaten up his confidence and that of the players. Wins increase confidence, and the more he wins, the more confidence his team will have; the opposite is the case for losses. Right now, the players don't have confidence anymore and he has a lot to do if he actually wants them to regain their confidence.