I don't think, Real Madrid have the power to cover this gap in their remaining matches because their midfield is not too strong for their strikers to score goals that will make them to recover from their losses. But it will be difficult for Real Madrid to win this title because Barcelona performance has showed that they have more opportunities to achieve this la Liga league title than Real Madrid in this season. If Real Madrid coach can introduce the strategies they used last season to defeated mighty teams in the champion league competition to play their remaining matches, I believe they can still achieve something good from the tournament.
Rather than trying in La Liga but have to hope that Barcelona will lose many points up to 12 points in last 12 matches, that is a little unrealistic hope, Real Madrid can simply focus on themselves in Champions League, match by match, opponent by opponent and win it.
In Champions League, they will meet Chelsea at the quarter final and they have diligent chance to beat Chelsea. What team will wait them in semi final? The opponent is either Manchester City and Bayern Munich and between two clubs, I think Bayern Munich are the opponent Real Madrid don't want to meet. They have some bad experience with Bayern Munich in Champions League but with Manchester City, Real Madrid will feel more comfortable.
If they go to final, opponent can be Napoli or Inter Milan.
Yes, Xavi must prove his capacity as a coach by giving the main title to Barcelona. But it looks like this season is really very relieved with his team. This season he has successfully won the Spanish Super Cup by beating Real Madrid in the final. In La Liga 90% maybe they have also tasted the sweetness of the most prestigious trophy
Xavi controlled his players well and united them as a solid squad to play as a whole team. So far, they have done great jobs together and see La Liga crown is more closely after each match day. However, in Barcelona, there are crisis with their finance and legal issues which are harmful for their club. Xavi can not control those things which are out of his responsibility. They must resolve those problems gradually to help the club future. With many young players, they have bright future ahead but only if they can convince those players to stay in Camp Nou.