It isn't the number of links that matter but the quality of links. Like a link from the USDA might count for more than a 1,000 blog links.
I have a site that usually ranks around number 8 - 7 in Google for a very competitive, high traffic (though unfortunately not high paying) phrase. My site has about 1,000 back links. The site at around position number 6 has back links in the low six figure range. The site at position one has back links in the mid 6 figures (500,000+). So sheer number of back links may help but they clearly aren't the only thing Google looks at.