Dave Weigel makes a point no one should ever forget:
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.
A man of the left certainly, but not a man of the Democratic Party -- the Richard J. Daleys of the party were among his worst enemies.
The simple version is that King became much easier for the Silent Majority to love once he was dead. No longer alive to demand that black people be able to buy homes in their neighborhoods, that workers be allowed to unionize and speak poignantly about American militarism bankrupting the country, money that would be better spent investing in poor and working people. Without death, there would have been no beatification of King. His voice silenced, it became much easier to pretend that all along, he had been saying the things we all wanted to hear.