Though staying visible is important, moderation is paramount.
Be warned of burn out. If you’re going to go to every networking event that comes your way and go on every interview, even if you don’t want the position, you’re going to start getting frustrated. Once you get frustrated, you become less genuine, and less effective. This is not good. It also does bad things to your relationships that you’ve had before you started networking like mad.
Concentrate your efforts on targeted opportunities where you will be able to connect with the right people, on jobs that you are properly qualified for an interested in. This will leave you less frustrated, which will make you happier, and more excited to talk to that person who will actually connect you with your dream job.
Oh… and as one of my best friends says… don’t forget to sleep, it works wonders.