Charles Franklin at Pollster.com takes some issue with this and places it into context.
Brooks is right, in that Obama's 16-point drop is the greatest of any first-term elected president since Nixon, Franklin finds: it barely beats out Bill Clinton's 14-point slide over the same time frame from 58 percent to 44 percent.
But if you take all the polls into account, not just the first and last ones, a linear regression will give you an aggregate rate of change over the time period, and Clinton takes it in that category: Obama has lost, on average, 1.6 percentage points of approval each month, while Clinton lost 2.3. Those two still have the biggest slides of any.
Some other presidents have done quite well. George W. Bush lost two percentage points, but Reagan, Eisenhower, Kennedy, and Nixon all made gains.
Here are the two graphs Franklin uses to demonstrate his point:
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