At what point in his first term did Reagan's approval drop "drastically low" during his first term?
It started to drop around July 1981:
http://online.wsj.com/public/resources/documents/info-presapp0605-31.html
It dropped into the high 30's by mid 1983.
You also need to look at the support for Reagan's policies at this time in his first term as compared to Obama's. There is a huge gap in Obama's popularity compared to his policies that is starting to be rectified. That wasn't the case with Reagan and hasn't been with most other Presidents. That rectification is trending against Obama and his policies, not in favor of them.
I'd like to see how this bizarre assertion can be quantified.
However, if you're going to take this tack, there's an alternative explanation that you haven't considered. You assume that everyone who disapproves of Obama disapproves for the same basic reasons. I can tell you that there are plenty of people who voted for him who now are dissatisfied with him because he hasn't kept his campaign promises, not because his policies are "socialist" or some such nonsense. I'm talking about things like promises of more open/transparent government, reforming health care, foreign policy, to name a few. For example, in the case of openness in government, Obama has taken the "Bushian" stand at nearly every turn. The health care "fix" is going to end up watered down to the point of being a slightly adjusted version of the disaster that we already have.
Ironically, it's the openly partisan liberal media that is taking him to task for lacking the courage to follow through. People like Olbermann and Bill Mahar have been quite vocal in criticizing him. I count myself as one of them. I give Obama a 3 out of 10 so far. But that doesn't mean I'm necessarily ready to vote Republican next time around, especially if they put up another candidate like Palin. The Republicans will be making a huge mistake if they interpret poll numbers as vindication of far right-wing populist policies.
"Reagan's recession" had been going on long before he took office, and was much further along then this one (stagflation had kicked in, while it hasn't yet in this recession). Also not long after his economic relief legislation was enacted (not until Autumn in his first year, if I remember correct) it showed signs of improvement which Obama's has not done (in fact showing, if anything, a negative effect).
You've omitted the most important factor at the time: monetary policies. You can give ownership of the 80's recession to Paul Volker, who raised interest rates in order to curb the runaway inflation of the late 70s. Then once inflation was under control, the Fed loosened the money supply, which had a major influence on the recovery. Asserting that the recovery was
solely the result of Reagan's tax cuts is simply untrue. While it was undoubtedly a factor, there is no way to measure the extent of it. I would argue that monetary policy was indeed the biggest factor, just as it was the primary factor in the financial and real estate bubbles of the 2000s. The problem today is that the Fed has nowhere to go this time around.