Adding on to what many have said already, it is possible though rare from what I hear! I was lucky to receive a full tuition scholarship for the MPA at the USC Price School. That did not include any housing or cost of living funding, but because it's a professional program I was able to continue working full time while doing the program. If I could go back, I would probably switch to the MPP in order to get more of the quant experience that will be helpful in the Poli Sci Ph.D.
If the Ph.D. is your ultimate goal, I would caution against paying for an expensive masters degree because many programs will offer that on the way to the Ph.D. anyway. On the other hand, if you can get into a masters program at a school where you would want to do your Ph.D., its sometimes possible to transfer in directly (or at least apply with more insider knowledge and the potential for some credits to transfer).