Obama has a very low approval rating among Republicans. Is that relevant?

Chart comes from here.

Nate Silver shed some light on presidential approval ratings by party yesterday, making a point that I've wanted to make for some time but couldn't since I don't have access to the mass of data (and probably wouldn't know where to look even if I did) that he has. That is, that at the time Obama has a very low approval rating among Republicans (27%) while George Bush (both Bushes actually) and Ronald Reagan had a higher approval rating among Democrats (around mid 30s to a tad over 40%). However, what makes the numbers a bit misleading is that it tends to give the impression that there's a dividing line among party affiliation right down the middle in American society, that 50% are Republican and 50% are Democrat and that sampling an equal number from each party gives an idea of how popular a President is.

However, since party affiliation always varies with the political climate this number doesn't always transfer into overall popularity. When party affiliation and morale is low, the ones that remain are generally pretty strict partisans, those that will stay with the party through thick and thin regardless of the political climate, and these people will naturally not approve of a president from the other party as much. As Nate writes:

Nonetheless, measurements of the partisan split in support for the President, as Pew Research has done here (they found a record partisan split in Obama's approval ratings, with 88 percent of Democrats but just 27 percent of Republicans approving of Obama's performance) are not quite as straightforward as they might seem. This is because partisan identification is at least somewhat fluid. The Republicans, in particular, have lost quite a bit of support over the past several years; those persons who continue to identify as Republicans are a hardened -- and very conservative -- lot. Just 24 percent of voters identified as Republican when Pew conducted this survey in March, which is roughly as low as that total has ever gotten.

This is also why bipartisanship doesn't really happen all that much when the other party is down in the dumps - because 1) the remaining party members are likely to be those that oppose the governing party/president the most, and 2) the remaining party members are in such small numbers anyway that benefits from bipartisanship are generally quite minimal.

One commenter below the main post mentions Simpson's Paradox, which is a good example of how seemingly simple numbers can often be misleading.