I don't know what LinkedIn you're using that provides you with job offers, but the one I'm on has only lead to recruiter contacts which may or may not lead to interviews, which (so far) have never lead to an actual job offer.
LinkedIn is great if you just want to endlessly socialize with recruiters. Don't worry about finding them: They'll all try to connect with you and chat you up about one of their jobs that is just like the one you have but at another company. Hell, you might even get an interview out of it, but good luck turning that into an actual job in today's picky environment.
And if any of those LinkedIn recruiters are reading this, Try This One Neat Trick That Candidates Love: Instead of approaching someone with a job posting that's basically what he did 2 years ago or what he's doing today, approach him with what he might want to be doing 2 years from now. You'll get better responses, I guarantee it.