Quote from Tsing Tao:
I am not a polling expert, so I cannot comment either way. But I have worked on a farm before, and I know the smell of manure when I smell it.
Imho, no need to be an expert. If you note that your sample of those who listened to the speech is skewed, by party affiliation, from a representative sample of the general population, you randomly subtract from the over-represented responses until your sample is again, by party affiliation, representative of the general population. Sure, the sample is going to be smaller, because many reps didn't listen to the speech, and many dems did, so you have a lot (if the sample is really skewed) to subtract. But, if the remaining sample is still large enough it will be statistically valid to the generally accepted margin of error.
Now, if you compare your sample's two party's responses to each other, you may find the dems overwhelmingly approved, but what you would not then find is that the reps overwhelmingly disapproved, because if that were the case you would not have a result of 91% for and 9% against.
From a "my team vs. your team" perspective, this poll's results are not encouraging or discouraging. The question was about approval for the president's ideas. Sure, most of us agree about those, he spoke vaguely about noble ideals. But, the methods to achieve those, there's the problem--the devil is in the details, and that was not part of the poll.