Short Answer: No.
Longer Answer: There are several compatibility issues, but the main one is that SRAM uses a 1:1 pull ration, whereas Shimano uses 2:1. Basically, Shimano and SRAM are never compatible as far as shifters and rear derailleurs go, with a few exceptions.
Here are your options: You can use a 9 speed shimano road shifter if you don't mind Tiagra, or if you can find and older shifter before the move to 10 speed. OR, if you want to stick with SRAM, the good news is that SRAM is moving some of its mountain groups to 10 speed, which means you will soon be able to use an X0 rear derailleur and cassette with a double tap shifter. Actually, you can already exchange derailleurs, so you can get a currently available XX cassette ($$$$$) or a more moderately priced IRD. It just has to be 10 speed.
SRAM is apparently aware of the desire to mix and match, and will soon be releasing Apex, which is a mid/entry level group with much of the tech of Rival only, heavier. It will have as an option a mid cage rear derailleur and 11-32 cassette.
Shimano is also apparently moving to 10 speed for the next generation XTR, XT, and possibly SLX, however availability will probably not be for a while.