Trump is the first choice of 19 percent of Republican voters, followed by Gov. Scott Walker of Wisconsin at 15 percent and Bush at 14 percent. In the sprawling and fragmented Republican field, the only other candidate to draw double-digit support was Ben Carson with 10 percent.
In the Democratic nomination contest, Clinton retains a large lead over Vermont Sen. Bernie Sanders, 59 percent to 25 percent. But that's down significantly from her 75 percent to 15 percent lead in June.
The poll contains mixed results for both parties. By 39 percent to 37 percent, Republicans have taken a slight lead when Americans are asked which party the next president should come from. By 67 percent to 30 percent, they say the next president should take a different approach from Obama rather than a similar approach.
At the same time, the public's tepid image of the Democratic Party is better than its strongly negative image of the GOP. Americans divide evenly, 38 percent to 38 percent, between favorable and unfavorable views of the Democrats. But their view of Republicans is lopsided: 28 percent positive, 44 percent negative. And by a 50 percent margin, they say government should do more rather than less to solve problems, a stance more closely matching the Democratic position.
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On issues, Americans favor Democrats by 15 percentage points on which party does better at "looking out for the middle class." They favor Republicans by 6 percentage points on dealing with the economy and 8 percentage points on foreign policy.
Americans hold slightly less optimistic views about the economy than earlier this year. Just 25 percent expect the economy to improve in the next year, compared to 21 percent in March.
The telephone survey of 1,000 adults, conducted July 26-30, carries a margin for error of 3.1 percentage points.