Doing it for the last three years on Wagerline consensus picks (those 60% favored or higher) would net you a result of 222-244-16.
Assuming you're playing a standard -110 line, you're looking at -244.2 units lost and +244 units gained for a loss of .2 units across the last three years combined.
So, in short, no. you can't fade all the picks and win.
http://www.wagerline.com/showprofile...&Sport=NFL