What about the little 'favourite star'? Surely that achieves the exact same thing ultimately?. I think, but I can't remember for sure, that the number of times a tweet has been favourited is returned by the api, so clients could show it if they wanted.
FWIW, I do not personally like the 'Like' button in Facebook at all. The most banal things get 'liked' which totally devalues it. A 'Does not like' button would have been more interesting :)