To tell you the truth, many people confuess finger strength with stamina. Stamina's what enables you to play for a long amount of time, not strength...if you look at a beginner guitarist they'll press down on the strings ten times harder than someone who's been playing for ten years, wasting a lot of energy. It's really all about accuracy and, in time, stamina will come and you'll be able to play for hours on end no problem (that's what I'm hoping anyway!)
Now, as for exercises:
Chromatics! In case you don't know what these are (sorry to be patrinising if you do) a chromatic note is one which is a semitone (1 fret) away from the last, i.e.

e|-0-1-2-3-4-5-6-7-8-9-10-11-12---

there's a very long (and probably difficult to start with) chromatic run.

Here's a very good exercise for you


D|-----------------1-2-3-4-- etc.
A|---------1-2-3-4----------
E|-1-2-3-4------------------

Sorry if this doesn't help...Take things slowly and make sure the notes are clear, then bring the tempo up...
Good luck!