When I first start my car in the morning it fires right up. After it has gotten up to temperature and is shut off, and cools it has a hard time starting back up. I have to put the pedal down to half throttle or so. Could my fuel injectors just be dirty or is this the sign of something worse.

 

could be a little dirty.

But try this:

http://www.rx7.com/techarticles_floodprev.html

If the problem is non-existent after a few cycles of trying the procedure, then chances are your injectors are due for a cleaning/flowing or replacement.