Jbartos,
Thanks for your input, but I already have the data sheets and they don't provide me with enough info to solve my problem. I've even e-mailed their technical support with no return.
Nbucska,
I wish I were drawing too much current, that would be easier to figure out. I've disconnected all the other circuitry from the supply and the 1555, with the same results.
F.Y.I.
I've even tried different values for the components(lower values for the capacitor and higher resistor values) with the same results. When I turn it on, the output stays low, and the voltage on the capacitor stays at around 1.1-1.2v with a supply voltage of 1.5v. I've replaced the 1555 with another one, with the same results.