I really can't see how they can lower the budget too much and still be true to the character. Spider-Man really relies on these over-the-top, larger than life, balls to wall brawls with colorful supervillains. There are things they can do like not film in New York, but it is always going to be a big CGI actionfest. That's what the franchise is.
Batman could get away with it by being more of a low key detective story and still be true to the character, but Spider-Man really can't. I think it will end up looking really cheap if they skimp on the budget.