36% (Newsweek)
The Chimp in Winter

Setting the limbo bar even lower, Newsweek has Bush's approval rating at 36 percent:

Only 36 percent of Americans approve of the job he is doing as president, and an astounding 68 percent of Americans are dissatisfied with the direction of the country—the highest in Bush’s presidency. But that’s not the worst of it for the 43rd president of the United States, a leader who rode comfortably to reelection just a year ago. Half of all Americans now believe he’s not “honest and ethical.”

Now is the autumn of Bush’s discontent, according to the NEWSWEEK poll, taken by phone of 1,002 Americans over Thursday and Friday nights. The president can take some solace in the fact that 42 percent of Americans believe he is honest and ethical. Only 29 percent believe that Vice President Dick Cheney is. And more than a quarter of Republicans, 26 percent, believe the vice president is not honest and ethical. The growing credibility gap could have ramifications across the president’s agenda: 56 percent of Americans say Bush “won’t be able to get much done;” only 36 percent say he “can be effective.”

[UPDATE - 5:50pm PST] Mrs. F just asked a good question--did Bill Clinton's approval rating ever get even close to being this low? Did a quick Google and found this great compendium of the major polls during the Clinton era (which includes all the polling data from sources like the Wall Street Journal, Pew, Gallup, CNN/Time, etc.). From a quick scan (and I invite you to parse all the numbers if you feel so inclined), it doesn't look like he ever fell below the 50 percent floor (again, I haven't looked at each and every number, so don't hold my feet too close to the flames). Hell, even Fox News had him above 60 percent save for four polling weeks (out of 59 polling weeks, which translates to just 7 percent of his presidency).

[UPDATE - 9:50am PST, 14 Nov] Whoops--forgot to add that poll compendium for Clinton: it's at PollingReport.com.