Weird, surely you noticed the TAs during undergrad? Did you think they were grading papers for fun? =P
I, along with most of the others I knew in science/engineering grad school, didn't really think that funding would ever be an issue, but I saw far to many cases in which it was.
I was under the impression that schools didn't want to accept someone who was going to drop out because of finances.
So basically if they thought you would not be able to pay, you wouldn't get in.
That said, I knew that funding would probably include things TAing, and that RA's were usually one of the better sources.
NSF said that from 93-96, only half of newly minted engineering phds graduated with debt, so the percent is a little higher than I thought.
NSF 96 debt info: http://www.nsf.gov/statistics/issuebrf/sib98318.htm