I was able to move the input to a different channel and the problem moved with the input, thus indicating my problem is with hardware I have connected.
In the mean time, I found an article entitled "Internal Analog Input Channels for Self-Diagnostics or the Monitoring of Analog Output Voltage" (found here: http://digital.ni.com/public.nsf/allkb/6c77b1884f5bbee8862569e3005be30e) that I was able to use to verify that my DAQ is indeed good.
Having read back through the user's manual again, I discovered that the power supply I was using had isolated outputs. Using a biasing resistor to AIGND solved my problem. My signals are measurable and stable where I want them.
Thanks for your input. I do appreciate it.