In answer to your question, "Have you heard any such sentiment [that Obama is unhinged] in your country?"

Not at all. There are people who like him and people who don't, but not based on his mental stability. Many of us do however think both the Republicans and Tea Party offshoot are certifiably batshit crazy and so are the people who elect them. It's only many of us here in Canada and not all of us because we have the 'Tea Party North' in our prime minister Stephen Harper and the Conservative Party of Canada. Nine years of that piece of garbage and with luck we get rid of him on October 19. It will not be soon enough for me.