Relocation Dilemma

I was recently offered a position in the ICU of a renowned/magnet hospital in the Orange County area of Southern California... I am very interested in taking the position, but unfortunately if I do, I'd have to leave my current unit (have been here for nearly 4 years!) with less than a 2-week notice. I have been trying to find work in So Cal for months now, and the offered position is one that is very much coveted, but I can't help feeling like slime for neglecting my fellow staff and management here. What do I do? I also wonder if this is unreasonable of the hiring ICU, as surely they must realize that leaving on such short notice will most-likely affect my managerial reference. I'm torn. Halp!