> Did a just low ball myself and ruin any chance of making more?

If by "making more" you mean "getting more for this particular position", then the answer is a definite *maybe*.

Remember there are other jobs out there, and other hiring companies. You decision isn't set in stone, nor is it fatal.

> Do I have any opportunity here to give them a new, higher number?

Certainly.

You could get back to this recruiter immediately, and indicate that after thinking it over you may have been too hasty with your answer. Now that you have had a chance to think about it, you realize that the range you would require is "x... y".

Be prepared to answer why you think this is the appropriate range (and not just because you are trying to squeeze out every last dollar). And be prepared to counter the feeling the recruiter might get that you aren't good under pressure.

Conversely, you could just leave your answer as is. Then, assuming the interviews go well and an offer comes your way, you can decide that it isn't enough at that point in time.

You might be able to point out that the requirements of the job are clearer now, and that based on those now-fully-understood requirements, you think you should get more.

Again, be prepared to fully discuss your reasoning. The risk you run is that you are considered flighty, not good under pressure, or overly cash-driven. You might also run the risk of pricing yourself out of the budgeted salary range.

In either case, the best that happens is that you land a job you want at a range you like.

The worst case is that you don't get the job at all, and are considered untrustworthy by people within the hiring company.