how low is too low?

Ignore the asking prices. Do your homework, come up with your fair number. Show the bid. Eventually, you will learn how low you can go. DO NOT get sucked into the nasty vortex perpitrated by the man, trying to steal the brothers jake!

You can offer whatever you think is reasonable. They can always tell you to f off.

Remember this, though--if you're renting today, you're dealing with TODAY'S prices, not the prices of four months from now. If you're convinced you can get a better deal four months from now, wait. If you choose not to wait, then you cannot expect to 'have your cake and eat it too' by getting a lease today at tomorrow's prices.

Sure, go ahead and negotiate. No harm in that. But do not expect a landlord to shave off 30% because of what MIGHT happen to prices sometime down the road. Ain't gonna work.

Where abouts are you looking?

South tribeca has 101 Warren, 200 Chambers with a lot of rental inventory and some quick price chops - 101 Warren has recently started closing which is when you got a rash of apts coming onto the rental market and it is some of these that have had the quick price chops already.

North has a mix of some new construction condos and older stock but it can seem quite desolate up there - but you might like that.

East is generally old classic lofts with lower prices. You should find "bargains" there.

FWIW, I have seen 1800 sqft 2BRS that could easily rent for $8000 to $9000 in the past have to cut prices maybe to $7000.
I would also expect a lot of negotiability in 101 Warren.

There is also 89 Murray - the rental part of the whole 101 Warren complex, which has 3BRS but they are more like 4 small bedrooms connected by narrow corridors, and there is also 88 Leonard but some here have described that as full of frat boys. I know 89 Murray is offering 1 month's free rent and I would bet 88 leonard is also.

Here is what I would pay:
For a standard rental building with doorman, no more than $4 a sq ft per month.
For a high end renovation with nice view, no more than $5 a sq ft per month.
Obviously, do not forget to discount the stated sq footage which is typically inflated by 10-20%.

http://www.streeteasy.com/nyc/rental/437387-condo-101-warren-street-tribeca-new-york