All of a sudden my front and back washer pumps have stopped working. When activating the spray function, both the front and back wipers work as normal, but the pumps do not. Neither pump makes the hum you would typically hear. Checked the fuse and it is in good condition. Working on getting in there to test for current, but am having trouble getting access to the wiring. Looking for any ideas as to what's going on.

You only have one pump, located in the engine compartment behind the windshield washer fluid reservoir, it likely is faulty. If you look in the FSM on page ww-7 it shows the location of the pump and it reads "front and rear washer motor".

The motor / pump is inexpensive, you can find one on ebay for as low as $10 shipped

Look in the FSM for more info
http://www.nicoclub.com/FSM/Armada/2008_Armada/ww.pdf

There is a youtube video of how to remove and replace the pump on a 2004 Armada but it should be the same or similar for the 2008 model
https://www.youtube.com/watch?v=ldCM0VTrtTE