The negative connotation depends on what you're using google and stackoverflow for. If you need to understand something that can't be directly reasoned through to come to an answer (random example: you need a description for an API call in some public web service) then there's nothing wrong with google, stackoverflow, etc being your first choice in search for your solution.
However, if it's a problem that -can- be directly reasoned through (random examples: any application logic issue, determining a regex to match a specific pattern, tree traversal issues, etc, etc) then your first choice should be to try to figure it out yourself before turning to the web. The rationale is twofold. 1) With enough practice, you'll often find you can solve your own issues faster than you can dig through websites trying to find someone else who has done the same. 2) Even if you ultimately can't find a solution on your own, attempting will at least exercise your brain and give you more experience, which feeds back into #1.
Another way of stating the rationale is that it helps to prevent cargo cult programming (see: http://en.wikipedia.org/wiki/Cargo_cult_programming). Even if you can't come up with a solution, or even if your solution is less than optimal, attempting to come up with your own answer first gives you a much better chance of understanding the underlying principles involved in the solution that google, stackoverflow, etc give you. That will minimize the chances that you apply the solution in a half-assed way that just causes you more problems down the road because you didn't fully understand its implications. It will help you in the long run.