Even if it is true, it's certainly not damaging to him. Really. Where's he have to go from here? The folks who hate his foreign policy have better reasons to hate his foreign policy already, and the dwindling (for other reasons) support he's got wouldn't dwindle any faster unless this affected the economy, which it wouldn't.
http://www.pollingreport.com/BushJob.htm
You'll note that very few respondents are in the 'unsure' category.