Here's a striking graphic of the results of continuing New York Times/CBS News polling on the question, "Do you think the federal government should guarantee health insurance for all Americans, or isn't this the responsibility of the federal government?"
Support for a government guarantee of health insurance starts dropping sharply as the country starts debating the topic. It's not clear from this graphic, provided by Gallup, but support is at 64 percent in June, 55 in July, and 51 in late September, well after the Long Hot August and just after President Obama's health care blitz that included his primetime speech to Congress and highly publicized rallies in Minnesota and Maryland. Note also that the question doesn't mention any downsides of the government guarantee; respondents apparently had figured those out for themselves.
Oddly enough, if you search the New York Times site for this question, nothing comes up. And if you Google the question, the Times isn't in the search results. It's almost as if they didn't want to publicize their very interesting finding. You can find a reference to it here and documentation here.
Another interesting take on support for health care "reform" can be found here -- a graph of all the polls on health care plans offered by the president or in Congress, from January to present, showing opposition rising. Also from pollster.com: President Obama's slipping approval numbers on health care.