PPP released numbers today arguing that little of the pushback against President Obama is coming from the left. To demonstrate this, they focused on the subset of people who self-identify as both liberal and Democrats in their poll:
Our new poll suggests that liberal unhappiness with Barack Obama is still largely anecdotal and not very widespread. His approval rating with liberal Democrats is 95%, with only 3% disapproving of him.
On health care 88% of voters in that group say they're with Obama and only 7% are opposed. We simply are not seeing any broad evidence of push back toward him from the left for not advocating for single payer.
One caveat to these numbers should be that not all people who self-identify as liberals in polls also self-identify as Democrats. Most self-identified liberals also self-identify as Democrats, but not all.
According to Gallup, during the first nine months of 2009, 20% of national adults self-identified as liberal. Also according to Gallup, during the first nine months of 2009, liberals were 37% of self-identified Democrats, 18% of self-identified Independents, and 4% of self-identified Republicans:

Using Gallup's national party IDs, and cross-multiplying to get the percentages to involved reach exactly 100% (some people refused to self-identify), that would mean 63% of self-identified liberals also self-identify as Democrats, 32% self-identify as Independents, and 5% self-identify as Republicans.
Currently, Gallup's weekly tracking poll shows President Obama with an 78% approval rating among all self-identified liberals. This includes an 89% job approval rating among liberal Democrats, and a 33% approval rating among moderate / liberal Republicans. Even though Gallup did not provide data for this subset, when combined with their yearly averages to date, these cross-tabs suggest President Obama has a 62-65% approval rating among self-identified Liberal Independents.
A 62-65% approval rating is still pretty high. The interesting point is that people who self-identify as both liberal and Independent diverge so sharply from people who self-identify as both liberal and Democratic. Partisanship within ideological groups seems to have a big impact on overall political outlook.
There is a substantial minority of self-identified liberals who disapprove of President Obama's job performance--most of them just happen not to self-identify as Democrats. In most cases, this is probably not because they think the Obama administration has not gone far enough to the left for its own sake, but rather because they don't see the country getting any better, and conclude that is because President Obama has not gone far enough to the left. Afghanistan probably isn't helping much, either.
Overall, Gallup estimates that about 4-5% of the country are liberals who do not approve of President Obama's job performance. This actually means President Obama is performing better among liberals than the Democratic Party as a whole. Once again, according to Gallup, about 8% of the country thinks that the Democratic Party is too conservative, although the poll used in that measurement had a far higher margin of error than all of the other polls listed here.
Previously, I estimated President Obama's job performance among the Democratic Presidential primary electorate to be 75%. Further, only about one-third of those who did not approve of President Obama self-identified as liberal. Currently, due to a slight drop in his overall approval among liberals, I would estimate President Obama's approval rating among the Democratic primary electorate to be 74%, with slightly more than one-third of those who do not approve self-identifying as liberals.
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