Gallup does a nice little public service and digs out the polling on MLK from the 1960s. Surprise: People started to loathe him.
Why was King so unpopular in 1966? You could read Taylor Branch or Rick Perlstein, and it is Friday, so you might have the time. The short version: In 1965 and 1966, King started working on housing in northern states, starting in Chicago. The 1966 Gallup poll here was taken around the time of the disastrous Marquette Park march, which King credited for the ugliest crowd of counter-protesters he'd ever seen. (We can read some hyperbole into that if we like.) He was starting in on his anti-war activism. He had moved on from the causes of Southern integration and voting rights to the far more volcanic issues of housing and red-lining and economic redistribution -- he became, fully, a man of the left.
King's subsequent political sainthood has very little to do with his post-Nobel Prize activism. It's left for guys like Cornel West to dig that up; to everyone else, King's "dream" was some easily-appropriated stuff about color-blindness.