It's difficult, but not impossible to sell a business within 3 months. I recently sold one within 2 weeks, but that's by no means a norm. First off, it will depend on the type of business you are selling. Secondly, and also very important, it will depend on the asking price. Remember, the true value of a business depends on a lot of things. In your case, time is of the essence, and I would recommend you sell it at a discounted rate in order to meet that need.
As for financing, there are usually a few different approaches that help to ensure you don't waste much time. First off, your Broker should have any potential buyers fill out at least some sort of financial information sheet so that you can see if there is even a chance of them being able to afford such a business as your own. Secondly, I would HIGHLY recommend you consider owner financing at least to some degree. In today's economy, it is very difficult to obtain funding from most banks and loan institutions. For certain businesses, it's nearly impossible.
In either case, you would also want to speak to a few banks and ask if they would be willing to finance a business such as your own. This will give you some indication as far as how difficult or possible it is for other potential buyer's to get financing.
Now, as far as choosing brokers, unfortunately, it is a very tough decision. I'm a broker, and I'll be first to admit I have not had good luck dealing with other brokers myself. There are several reasons for that, but that is beyond the point. I would tell you to research the brokers you are considering, and interview them. Ask what kind of marketing plan they have, ask to see sample non-disclosure agreements, and what process they use in selling your business in general. That should give you at least some sort of idea of the professionalism of the broker(s).
Hope this helps. If you need any other help or advice, please feel free to contact me at firstname.lastname@example.org