Wow, big family or not, that is totally insane.
My family is enormous - DH's parents both have more than six siblings (and all the attendent children, in-laws, cousins, etc). I am one of nine children in my family. But even with our gigantic clan we can easily get a list down to 50 women for a baby shower...
100 people is NOT a baby shower, it's a cocktail party in honor of a baby. I mean, she cannot open 100 gifts - it would take forever. Gosh, I'd pay NOT to sit through that gift-opening.
Unfortunately, now that you've already given over control of the guest list, I think you have to be honest about what's happening:
"I am so excited about your shower! I planned my budget, and I have $X available for the party... That means we have $Y per person for food and drink, including decorations and invitations - I know it's not a lot. I mean... I can envision doing it with twice that much, but... I so hate to do it, but in order to give you the party you deserve we'll have to figure out a way to make the list smaller. The good news is, if we could get it down to Z number of people, we'd have the amount we needed to do your party in the style it deserves!"
Then, have a plan for her possible reactions, since she may not say, "Oh, in that case, we can cut Tim, Sue, Larry..." Be firm in deflecting any suggestions that you aren't comfortable with and you'll be fine! She may honestly have no clue how much invitations, postage, alcohol, food, etc, really add up to - especially if she's young and hasn't thrown many parties herself.
Next time, I'd recommend giving MTB a specific number of invitations you can extend. Build in the assumption that only about 2/3rds will attend: if 30 is your number, tell her she can invite 45, etc. Too little, too late, I know... :-P