We have 300 followers right now, and I'm going to about 15% of our Likes are SPAM. A problem, but not completely overrunning the system. They seem to also be using Tumblr tag pages to find articles to like. Articles tagged with common product keywords like handbags, shoes, or a brand name get much more SPAM Like activity than other posts.
Tumblr does seem to be hiding the entries in the Dashboard for some of these, indicating that they have some sort of system in place for isolating spammers.