I think Godwins Law is a useful law. It was framed essentially to highlight the number of times people will draw extreme or absurd analogies to Hitler or the Nazis, in an attempt to further their case.
In a conversation about euthanasia however, Godwins Law does not apply simply because euthanasia was part of the Nazi programme and is therefore very relevant.
As for this councillor - A couple of points. As an experienced councillor, used to dealing with lobby groups, members of the public and speaking in public, he was very unprofessional voicing his comments in public the way he did, especially to the people he expressed it to. Secondly - reading the transcript, he sounds very confused to me. On the one hand, he appears to be suggesting that it would be acceptable to him if some severely disabled children were to be euthanised - "just like farmers with their sheep, running around with 2 heads or 5 legs"- because they represented too great a burden in terms of financial support to them and their carers. On the other hand, he says that he is "against abortion" and "could not kill a fly" or words to that effect.
Even the suggestion that we should euthanise children because of profound disability is morally and ethically repugnant. These are humans beings we are talking about, not a farm animal like sheep. The mark of any civilised society- the mark of any civilised human being- is to support the halt and the sick and the lame.
He may have misspoke, but I believe he holds such a view, muddled though it is from his own transcript, and I am quite surprised myself he was re-elected.