Everyone seems to be asking themselves how long Obama has before the American people start getting -- as Andrew Sullivan puts it -- pissy. Nate Silver looks at polling data and guesses that it will be a year and a half. Blumenthal is skeptical, but not very specific.
I'd like to approach the question not from current poll data but from historical analogy. The other harsh recession since the great depression was the 1981-82 slump, when Reagan was in power. Like Reagan, Obama is a President with a pretty strong connection to the American people, so the comparison is apt that way. Let's look at the unemployment rate since that seems to be the measure that's most connected to popular anxiety, even if it is a trailing indicator for the economy.
Unemployment started going up in July 1981 and peaked in December 1982. Reagan's popularity bottomed around 45% in January of 1983, so it never really cratered. It was above 50% until October 1982. That seems to confirm Nate Silver's guess: about a year and a half, maybe a little less. I would just add two things: Reagan's recession began during his term. He was quite effective in blaming it on Carter, but the timing surely didn't help him. Obama's recession is more closely identified with his predecessor because it was already a year old when he stood on the Capitol steps to take the oath. Also, I would note how fast Reagan's popularity rebounded as the economy improved. Even though the unemployment rate was still above 10% half way through 1983, the economy was showing signs of recovery, so his approval rating was steaming back up to 60% by the fall of that year. Which is to say, if we start getting a visible recovery by Spring 2010, Obama's numbers may not fall below 50% at all.