The poll found just 38 percent of Americans wanted the US Senate to confirm Kavanaugh, while 39 percent said he should not be confirmed, and the rest were undecided.
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The only two nominees with weaker support were Harriet Miers, who withdrew her nomination in 2005, and Robert Bork, who was rejected by the Senate in 1987.
US President Donald Trump announced the nomination of Kavanaugh on July 9 to replace justice Anthony Kennedy, who stepped down from the high court.
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The poll was conducted between August 26-29 with a sample of 1,003 adults and has an error of 3.6 percentage points.