It depends.  If you were interviewing with someone like me, it could be a mark against you, but I go all the way back to when the internet was text-based and you had to telnet into a BBS if you wanted to do anything.

If I were interviewing you, I might ask some follow up questions like:

 - Why wouldn't you ask a coworker?
 - How would you ask a question without revealing company information?
 - Why wouldn't you be able to find an answer on your own, instead of asking questions.
 - Ok, you ask a question on SO, and someone gives you an answer.  What happens when that code breaks?

 
I would be concerned that you wouldn't be writing your own code, but cutting and pasting snippets of someone else's code, and thus wouldn't know how to maintain that code.  I come across this more and more frequently these days.  The worst case scenario is we end up with a Frankenstein's monster of lumbering spaghetti code that nobody knows how to maintain.

So, a better answer would be:

> I isolate the piece of code that does not work and try to change to make it work, then I step through the code.  If at that point, it still doesn't work, I would check online to see if if I can find any articles discussing that issue.  Failing that, I would consult a coworker, as a fresh pair of eyes often helps

or something like that.

The point being that you want to demonstrate your thought process.  An answer like that would demonstrate to me that you have problem solving skills, and try to solve your problems on your own before going out to find answers, and then consulting with others as a last resort.

That would show me that you are both independent, but not to the point of being too proud.