I have sent thousands of CVs without getting a single interview. I did that for 5 years till I finally concluded it wouldn't work. What I needed was a couple of minutes of attention from the guy in charge of recruitment at a specific company. And that's it. I gathered as much info about the company, spoke with a guy I know already hired by that company and finally made the call. I hadn't even applied nor sent them my CV because I didn't think I had a chance. But I got hired.
What I've learnt from this is that thousands of CV's cannot compete with a phone call to the right guy. If everybody sends as many CVs as myself, just imagine how many CVs a company has to go through. They will have to hire extra personell just to read them all. Not gonna happen. People who get hired has one thing in common, they have all managed to stand out of the crowd, and I have heard many stories common to my own. Actually I believe that not applying and not sending CVs, but calling and showing up in person is the way to land a job.