I did this in the UK and it felt like a huge deal. I wasn't yet a developer at the time, but I think my experience is still relevant. It seemed to really have an impact on interviews. The interviewer would end up asking a lot of questions about why I left the previous job (it was for quite innocent reasons), rather than the stuff I really wanted to be talking about, which puts the whole thing on a downer from the start. It affected me a lot, which meant I started to become very nervous before interviews, so performed badly, got even more nervous, etc. I pretty much have a phobia of interviews to this day (almost 10 years later) because of it.
I think the answer to the original question depends enormously on what type of person you are. If you're extremely confident in yourself, and in your skills, and you're naturally positive and optimistic then you should be fine.
If you have the sort of personality that tends towards introspection and self-doubt, then think very carefully before doing this. Think about how you'll feel after your 10th rejection, or when your savings are starting to run low. Will you still bounce back?
Finally, I've heard that some recruiters use your current employment status as a filtering criterion. So your CV might not even get looked at. This is insane, but I've heard it enough times to think it might be true.