Here is a chart featuring the all-time worst Gallup poll results for every president over the past 70 years:
Note that I mentioned above how Truman's highest disapproval was 67%, but here it is listed as 65%. This is because, for the purposes of this table, I took the single poll for each President that resulted in the lowest overall approval / disapproval margin. Truman's overall worst gap was -45, but it did not come from a single poll. Nxon's overall worst gap was -43, but it did not come from a single poll.
Update: As noted in the comments by Max Fletcher, remarkably, no President had a negative approval / disapproval margin from February 1953-March 1966. In fact, every poll taken during that time period registered at least double-digit approval for the sitting President. No wonder the late sixties are viewed as such a tumultuous time in America, as they were clearly following the most remarkable period of general contentedness we have ever seen. For the flip side, from April 1966 through August 1983, presidential approval ratings were in the net negative more than half of the time.