Over at Pollster.com, Brendan Nyhan has reviewed trends in support for health care reform in the weeks following President Obama's speech to Congress. Nyhan acknowledges some short-term upticks in support, but concludes that in the long run, support has not changed all that much.
I decided to pursue this question too, but by breaking out the support levels from particular polls individually. The following chart (which you may click on to enlarge) is a bit busy! A couple of things to note are that the widths of the color-coded rectangles correspond to the days a given poll was in the field, and that the vertical gray bar represents the day of Obama's speech.
The trends in support appear similar to those in Nyhan's analysis. As can be seen in the above graph, polls from the Economist/YouGov (here and here), Rasmussen, and FOX News all show mid-September slides, probably a fall-off after the post-speech bounce.
However, Rasmussen, Gallup, and AP-GfK all appear to show early-October resurgences (a little less clear in the case of AP-GfK, as it doesn't have a mid-September data point). The Economist/YouGov poll from late September shows stabilization (although not gain) after its earlier polls showed a drop in support. The next Economist/YouGov poll, which should be out shortly, potentially could corroborate other polls showing an October rise in support.
Whereas Nyhan identified a trend of rising opposition to Obama's and the Democrats' reform plans, some of the newer polls (not graphed here) appear to suggest otherwise. Gallup showed opposition (i.e., the percent of respondents who would advise their members of Congress to vote against) falling from 40% in mid-September to 36% in early October, while AP-GfK found less disapproval of Obama's handling of health care in October (47%) than in September (52%).