If history serves as a guide once again on these two issues, Obama is probably in more serious trouble than the polls generally indicate. Now before people say I'm drawing too many conclusions, just review the RCP charts and you'll see how often 47% appears in the horserace and job approval. It's hard to miss.
I don't disagree that he's at around 47%. But where I think you're drawing too many conclusions is the premise that history serves as a guide. We do not have anywhere near a statistically useful sample of elections (with polling data) in which the incumbent was below 50%, much less those in which he was below 50% but very near it.