Amy - the question of "wiggle room" is going to be dependent on so many different options it would be wise to consider working with an agent (if you are not already) who is familiar with your area.
If you provide more information it would help answering your question. Are you paying cash or financing? Is the home bank owned, owned out right by someone or does someone have a mortgage on it? Has your agent (if you have one) done a Competitive Market Analysis to determine the true market value? Is the listing price above or below the market value? All of these answers will help in determining how much room there is on the asking price. Could be they're asking way too much, could be that they're way below market value waiting for someone to snatch it up.
Your best bet would be to treat this like any other home purchase, find a good agent, and take it step by step. If you don't have an agent and refuse to get one, you could always have a bank appraise the house (a few hundred dollars, maybe 500) and see what they would loan on it. That will be an excellent way for you to determine how much room there is on the price, if any. If you are financing, you will have to get this appraisal done anyway, so make sure you use an appraiser from the bank you plan to get your loan with, so you don't end up paying twice.
Best of luck!