Real Madrid certainly needs to win trophies next season. Failure to do so will undoubtedly disappoint some of their supporters. However, given Real Madrid's vast experience and numerous trophy winnings, there's certainly a chance they can bounce back next season, even though Barcelona is currently in good form.
It's true that if Real Madrid can maintain their strong performance, they have the potential to win numerous trophies. If no Real Madrid players are injured, they certainly have a chance to win many trophies. However, Alonso certainly has the potential to improve Real Madrid, as he has undoubtedly witnessed it since Ancelotti took over. We'll have to see whether Alonso can lead Real Madrid to another trophy-winning season. Most importantly, I hope Alonso can ensure Real Madrid's star players continue to play well and avoid any selfishness.
It would be more than just upset, fans would be rioting. Real Madrid, after spending this much money and getting this awesome team together, can't afford to lose one more time. They are aware that they can't have a great team all the time, so this is that third Galaticos they built, and need success. First was that famous Zidane, Beckham, Carlos, Ronaldo etc period, second one was Marcelo, Ramos, Kroos, Modric, Ronaldo etc period, and now this is the third one and they need to be great.
Sure, there are periods where they go from one to another where they rebuild and may lose a few years, but this is now the best team they will have for the next five years, and they need to win as much as they possibly could to make this mean something.