The lesson here isn't that spamming works - it does now, but it'll very soon stop working if everyone does it. The real lesson is that applying for positions at companies that you want to work at, even if they aren't advertising the job you do, works. Send them your resume regardless and see what happens.
Meanwhile unemployment benefits in certain countries (e.g. Australia) legally require you to do this to keep your benefits. Literally applying.
On the one hand I get that you need to require them to do something and I don't have an immediately better idea, but on the other hand they keep talking about increasing the number of jobs you have to apply for etc despite their literally not being enough jobs for everyone on benefits.
During the height of the recession I had to do the same (also US).
After a while you can tell that a good number of those positions are just recruiting firm honeypots; which makes the search both aggravating and depressing (since you feel like there aren't any /real/ jobs out there).