As I recall JJ and friends have only spent what Paramount GAVE them to spend. I don't believe that they went over budget or that Paramount is scrambling to try to cover unexpected costs...
It's a producer's job to secure funds. They gave him what they asked for. I doubt very seriously they said "here's 150 mil. Think you can spend it?"
As I recall, the head of Paramount at the time Abrams took on this project was an admitted Star Trek fan. I'm sure the idea sounded good to him at the time.
Then again, as I've said before, if it weren't for the success of Lost, this movie, with the exaxt same story and cast, would be a direct to video feature.