It's most definitely do-able, but the question is whether such a constraint would affect the look/scale of the film. TF1 was around 150, but Bay had massive connections within ILM and the military to keep costs down. ST was 150, but also had plenty of green-screen and studio backlot shootings.
Anything that's shot real, and is massive in scale, will always take up the majority of that budget. Look at Nolan's Batman films. Nothing really extravagant, but shooting in places like Hong Kong and Chicago, in the busiest districts, don't come cheap. I don't presume someone of Nolan's indie sensibilities to ask for, or spend money in an unnecessary manner.
You are right with anything in the 200+ range, though. I'm looking at Pirates and Spidey.
Avatar I'll make an exception for since it's always expensive to fund next-gen technology.