They have or will focus group this, and the focus groups will probably say not to go there. However, I don't think it will hurt to hear that the right wing on the Internet keeps on saying it, especially since it is basically true (to be completely true, insert "self-described" right before the phrase "war criminal" above, and drop the word "average").
Now, on DU they will keep saying Bush is a deserter, and mainstream press will report both charges, implying that the extreme left and right partisans deserve each other. However, I'm hoping that only the true charge will stick.