If I don't put any salary for me in the budget (so I stay on my current day job and will be developing the game in my free time), reduce the amount of content and stick to the most necessary expenses only, then I can make it with $2000, I guess. But maybe all that sacrifices are needless and maybe I can be so bold to ask for a bigger sum not fearing to scare off the publishers.
Publishers aren't scared about spending money, that's their job. They're scared about not getting it back.
How much they're willing to spend depends on
Game concept
How far along it is
How much they think it will sale for, and how fast
External Factors (haloween themed near halloween = bonus)
You need to think about way more than the amount you need to finish the game.. and make a budget. "I guess" will not convince anyone to loan you money.