Poetry and prose do not operate by identical fair-use standards because, in general, poetry contains many fewer words. According to nearly everything I have read about fair use of poetry, you should not quote more than a stanza unless you are writing a book review, and even then you should be careful. Copying someone else's entire poem onto your blog is stealing, unless it's in the public domain (published before 1923) or you get permission from the rights' holder: that is, the poet, the publisher, the author's representative, or the estate.
I want to say that I don't presently have a personal beef with anyone about illegally copying my work. I've simply been noticing how rampant this practice is, and I think people should have better manners. Even though most poets don't expect to make money off our work, civility is not only a comfort but our right. Ask to copy my poem, and I will most likely say yes, and my publishers will most likely say yes, and we won't charge you to do so. Ask is the important element here.
But some poets and their publishers do expect to make money off reprints. So if the blog owner doesn't want to pay that fee, then he or she should do some research and find another, more flexible poet to feature. There are a lot of poets in this world, and many are just as interesting as the famous ones are. Many of them are more interesting.