Your second idea, about the session ID, was one worth pursuing. So I tried the URL manually, and I got a search page. I tried removing the "session ID" and I got a page with just 2 links: to a plain search page, and to an advanced search page. Apparently it's the latter the OP has been using, and its canonical URL is http://www.stat-usa.gov/nct_all.nsf/advSearch.

And when I looked in this page's source, the form's action attribute was /nct_all.nsf/2d58b7a34bbaa3838525703f004f804e?CreateDocument: the exact same strange weird ID. So no, apparently it's not variable, but likely, generated by their web site creation tool.

Do note the part after the question mark: "CreateDocument". I propose the OP tries it using POST with this part appended — and obviously, this wouldn't work with GET.

I did try the OP's code as posted at this time, with just this changed (and the broken up words reassembled), and it works for me.