Is the existing offer low because the employer's expectations aren't realistic with respect to the position and salary range, or because you are much better than the average employee for that position and the hiring manager has failed to recognize how wonderful you are?
Whatever the answer is, that tells you what you need to address - e.g., explaining how/why the market is not what the employer thinks it is, or why you're so special that you ought to be paid above average wages for the position.
Neither of those is necessarily an easy sell, but you should at least be able to identify the basic difference between your view of the situation and the employer's.
Also, make sure you really want what you're asking for - when a candidate wants to negotiate with me to come in at the top of the salary range (or beyond), if I agree to the higher number, I will have correspondingly increased expectations regarding productivity and reduced time to get to that level of productivity after starting. If you're going to ask for more than what's standard, you had better be prepared to give more value than what's standard.
When money gets tight, the people whose perceived value is low relative to their perceived cost will get let go first.
It might be better to have a job at 90 or 95% of your desired salary where you're performing at your employer's expectations and your job is not at risk, than a job at 100 or 110% of your desired salary where you're in a constant struggle to justify your continued employment.
Also, your salary needs to make sense in the context of the other people in the organization - if you are going to ask for more than your supervisor makes, you'd better have something really special going on. It also might be political suicide for you (or your supervisor) to cross some unknown (to you) line in the sand related to someone else's salary. I remember sitting in on an interview when some random sales monkey announced that he expected to be paid an amount that was around 2x what our CEO was making, and after a good laugh all around the table the interview ended more or less immediately, to the great surprise and disappointment of the sales monkey. What the sales monkey wanted was probably reasonable for a really good salesperson on a commission/performance basis at a big company - but it was ridiculous for a fixed salary for a new hire at a 15-person startup where everyone assembled their own particle-board desks and wore jeans to work.