Unless you are going at a particularly high-demand time, Priceline would probably work. See betterbidding.com . However, it's probably too early to put in a bid.
Although I definitely favour doing things cheaply, Amsterdam hotels that are low-budget tend to be quite awful, and not "cheap and cheerful".
But still, take a look at kayak.com and hotelscombined.com for your dates.
Also, you can consider staying in outlying towns like Haarlem, Utrecht, or Leiden. All are highly attractive places in their own right, and convenient to Amsterdam.