Their second leg against Barcelona in copa del Rey will be surely very important and they will put all efforts to win this match not only because it's the only local competition left for them but also because Barcelona dominated the last matches against real Madrid and they will surely play for a revenge
I think that most likely will not be the case,Real has only one objective right now for this season and it is the Champions League,they will be playing next week there and I think that despite their opponent looks easy based on their recent form as Chelsea is losing a lot of games,it won't be easy for Real Madrid.They have very slim chances to make a comeback in the second leg of the Copa del Rey and as such I doubt they will be trying hard in this game.The only way they turn things around is if they find a weak and not focused Barcelona but we all know that rarely we see a non focused Barcelona when playing against Real Madrid.
Of course it would be very embarrassing for Real Madrid if they didn't want to fight again in the Copa Del Rey. This season, Madrid's honor was torn apart by Barcelona. In La Liga they were beaten twice by their eternal rival, then Madrid were also defeated in the Spanish Super Cup final and the first leg of the Copa del Rey. So because of that, I'm sure Real Madrid will exert their best strength in Leg 2 later. I think the Copa del Rey is the only chance for Madrid to keep the honor in Spain this season. The Champions League is of course also a top priority but against Chelsea is not as hard as facing Barcelona, because the prestige of El Clasico is more meaningful than the others.