WinterSolstice, I am in the exact same position as you regarding both Elliott and SAIS so I am so glad you started this thread! I have always assumed that taking out loans was going to be a given, but then reading some of these posts, I wondered if I should even attend grad school next year at all and just wait and re-apply. However, I do feel that grad school is the appropriate next step for me both professionally and personally, and I don't want to work for another 2 to 4 years in a field I don't like just to save up more money, or on the off-chance that I might magically get more aid the next time around - who knows, there could be even more competitive candidates applying during the next application cycle.
I'm planning on calling the financial aid offices at both schools and asking what percentage of their second year students receive funding - that will be a big deciding factor me. As it stands right now, I'll just suck it up and take out loans for the first year, and apply like crazy for any and all fellowships (both within and outside the school) for the second year. I'm also planning on getting a part time job on the side to help offset living expenses and cut down my overall debt - I did this during a semester in DC a few years ago, and while it was difficult, I was able to provide for my rent and food on under $1000 a month. I didn't get to go to the bar as often as some of my friends and I got really good at thrift shopping for my clothes, but it's worth the sacrifice.
In the end it's all about opportunity cost, and only you can decide what that is for your personal situation.