But here's what else we can say about these Sanders backers: Many of them will vote for Clinton while holding their noses.

Just 47 percent of them say she is more honest and truthful than Trump. Another 16 percent of Sanders backers actually give the nod to Trump on that count, while 35 percent say neither is more honest and truthful.

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By contrast, 64 percent of Republicans who voted for someone not named Trump in the GOP primaries still say he's more honest and truthful than Clinton.

Sanders backers have an equally gloomy view of Clinton's capacity for changing things in Washington: just 18 percent say they think Clinton will change things for the better in Washington, while 70 percent say she "wouldn't change much."

Again, supporters of Trump's primary opponents are much friendlier to him on this count. A majority -- 52 percent -- say he would change things for the better.

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The lack of confidence in Clinton's ability to improve how business is done in Washington is also laid bare in the responses to another Pew question. The pollster asked whether Clinton or Trump would do better at reducing the influence of special interests. Again, only a plurality of Sanders backers (46 percent) picked Clinton, while a similar share split between Trump (27 percent) and neither (23 percent).

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Clinton does do better among Sanders backers on measures such as readiness to be president, along with defending the nation from terror attacks and helping the economy -- all important things that are clearly winning her votes. But it's clear that where Sanders backers continue to have reservations with her, and it's all about her inability to do what the Vermont senator promised and to change how business is done in the nation's capital.