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The poll showed steady support for Mr. Johnson, the Libertarian Party nominee — but he did not build on his July number, suggesting he may have plateaued.

In order to secure a spot in the presidential debates, he will have to get at least 15 percent support in a cross section of polls, according to the rules laid down by the bipartisan commission that arranges the debates.

As for Mr. Obama and Mr. Romney, their supporters are warming to them. In July’s survey, only 57 percent of Mr. Obama’s supporters said they were voting for him because they thought he was the best man for the job — as opposed to simply being the lesser of two evils, or a vote against his opponent.

About 51 percent of Mr. Romney’s supporters said he was the best pick.

But in the latest survey, 66 percent of each man’s supporters now say they are backing their choice because he is the best candidate for the job.

The poll has a margin of error of 3.5 percentage points. In this poll, which was weighted for demographic purposes, those who didn’t have a definitive choice for president were asked which way they leaned, and those were included in the head-to-head tally.