I'll, probably, go way further into the specifics of this down the road. Probably. But, for today, this is a high-level summary of do's and don'ts when approaching a production that is underfunded. You're not a low-budget project, you're producing an over-promised creative given the budget you have to work with. Notice the difference.
First question--do you have needs for specialty equipment, mounds of extras, special props or set building? Now, take your greatest weakness (a big art need, with no art money) and find a way to make it a positive. How? Well, it depends on your situation, but here are a few, probably useless, examples:
1. Creative calls for a weird location. You need to build it. Or maybe, you need to find the best/weirdest/oldest/most salty location scout out there to crack the door on a place that's 99% what you need. Then, Art monies become location monies, and I'm sure you can negotiate out some leftovers to spread around.
2. Use your director. Get your director drunk on booze, or their own creativity and get the seed planted that we can/could/should talk about tweaking things a bit. Maybe a more vacuous space would keep focus on the principals struggle. Maybe a vacuous space just means a big empty room. Cha-ching!!!
3. Use your cunning, people skills and rapier wit to dupe your colleagues into making decisions that positively impact your budget. Don't be passive. If you just sit around waiting for your director to talk, she or he will run your face into the ground (metaphorically, and possibly physically).
No. Just give them what's in the budget. Nobody will ever fault you for that.
FEED THE CREW TACO BELL
Don't. Not only will they hate you, but they'll be sluggish and testy for the rest of the day due to malnourishment. Not the place to save...
The biggest threat to your budget isn't adding a lens, or a crane, or 668ft of unexplainable circle track...it's time. Time is what will F#%k your budget. If you start getting behind, the AD starts pushing (that's his job), so do you, so do all the keys, so does the Director--and THIS, this is when we go into overtime or worse...people get hurt. An injury on-set will piss off your EP/Head of Production/whoever you care about impressing more than anything. And that safety (or lack of) falls to the AD, but ultimately, to you who orchestrated it all.
So, here's my advice. Be damn smart. Smart as hell. Make smart deals with vendors, locations and fabricators. Once you're done with that--get cozy with the best damn AD you can find, and get on the same page. If you-two are connected, the train will depart and arrive as scheduled, and the biggest of all budget blunders (accidents and overtime) will escape you.