My roommate, Chris, and I just completed our own level 2 Menger sponge origami project, built from 3456 business cards in something around 31 total working hours spread over 4 days (click picture for more pictures):
In all honesty, they weren't exactly business cards. A shortish chain of relations gets Chris and I to a guy with access to card stock and an industrial paper cutter, or so. For Christmas we got 4000 cards cut. They're business card size, and I think approximately the same weight. But then, I don't interact too much with business cards, so I could be mistaken.
Anyway, I should stop rambling. This is not our first large-scale origami project. A few summers ago, Chris and I, along with a then-first-year graduate student (Sean) in the department, built a modular torus:
It was a fun project, but didn't hold up under it's own weight. And since we couldn't find a place to put it, it sadly didn't last long. What's more sad about that is that we didn't even light it on fire, which would have looked simply amazing, I reckon. But, again, I digress.
So, this big sponge. It was most recently inspired by Thomas Hull's Project Origami book, but it's possible I'd heard about it before reading said book. On my sister site, I posted my calculations for finding the formula for the number of cards needed, so you can check that out, if you are interested. And over at picasa, I made an album of some of the pictures I took, which is probably more interesting. I'd also like to direct you to this picture, of somebody else's project, because they also made an 'anti-sponge', which looks awesome (like I needed another project).
In the process of building this sponge, I decided this (well, perhaps the smaller level 1 sponge) might just be the best modular origami project for somebody just starting to do modular origami. The pieces are very easy to fold (just 2 creases per unit), and pretty forgiving (if you're folds aren't quite as accurate as they could be, it should still go together pretty well). The pieces are fairly easy to put together (though, of course, it takes a little practice) - in particular because the whole thing won't fall apart if you unfold part of one piece in order to stick another piece somewhere. The final result is very nice and quite sturdy. So, if you are just starting modular origami, you might consider making this model. I recommend Hull's book, but you could probably find resources online for instructions putting these together. If you're looking for other modular origami books, my favorite is probably Tomoko Fuse's 'Unit Origami'.
I know the lighting is pretty poor in this picture, but I like it anyway:
I can't wait to take this thing outside and balance it on my chin :)