He is under pressure because he has yet to get the better of Barcelona. The fans are divided, but I do believe most favour him as can be heard by the Jose Mourinho chants at the Bernabeu. The ones booing him are probably Pathetico and Catalan fans in disguise or something.
I am sure Perez will not fire him unless he ends up losing La Liga. Forget the Champions League, but if Mourinho lets slip this 10 point gap, then the press will pretty much force Perez to make the decision. Thats how it is in Madrid.
However I do not think Mou will let that happen, and given the way we have played this season, even I don't see us dropping 10 (or even 9) points. Even if we do, it would be only matter if Barcelona somehow manage to win all their remaining games. Given their woeful away form, the chances of that happening is actually much higher than us droppoing points.