NOW is in the wrong fight. The issues should be about access to affordable healthcare and jobs. Without addressing these issues, NOW and others have nothing to offer the average Jane and in consequence, have allowed Sarah Palin and her elk to define women's issues.
There's nothing in the comment to suggest that this substitution was the result of intentional wordplay, but it's hard not to think that the slip was influenced by Palin's well-documented love of hunting big game in Alaska like moose and caribou. (Not sure about the elk, though. See Bill Poser's post and comments thereon for an explanation of the difference between North American moose and elk.) And perhaps the commenter is from a part of the country where milk is pronounced as [mɛlk] (say, Pittsburgh, Utah, or Washington State), rendering ilk and elk homophonous, or nearly so. Add the fact that ilk is a low-frequency word that lingers in crystallized idiomatic usage ("of X's ilk," "X and his/her/its/their ilk"), and it's clear to see that this is a prime candidate for eggcornization.
[Update: Commenters suggest that speakers of dialects where milk is pronounced as [mɛlk] may still pronounce ilk as [ɪlk]. So this seems to be a case of lexical diffusion where the sound change spreads variably depending on how common the word is — much as speakers who lack the cot-caught merger may pronounce dog with the caught vowel but less common -og words like blog with the cot vowel. More on that point here.