Vice President Joe Biden, who has not declared ambitions, but told ABC News "there is a chance" earlier this year, is second in the poll with 16 percent. Vermont Senator Bernie Sanders, running as a Democrat, rounds out the top three with 14 percent.
In the more crowded Republican field, Bush and billionaire Donald Trump are leading the pack with 19 percent and 12 percent apiece, the only candidates with double digits. Both put their hats in the race earlier in June.
Terrorism topped the issue poll respondents were most concerned about, with 48 percent, followed by health care (44 percent) and the economy (47 percent). Foreign policy, illegal immigration, race relations and same-sex marriage were in the 20-30 percent range.