The survey (pdf), conducted June 15-19, presented 803 registered voters with six possible running mates for Clinton: Sen. Cory Booker (D-N.J.), Sen. Bernie Sanders (I-Vt.), Sen. Elizabeth Warren (D-Mass.), Housing and Urban Development Secretary Julián Castro, Sen. Tim Kain (D-Va.), and Sen. Al Franken (D-Minn.).
Sanders had the best effect for the former secretary of state, with 39 percent saying they'd be more likely to support the Democratic ticket if Clinton chose him as her running mate. Twenty percent said the choice would make them less likely to support Clinton, while 39 percent said it would have no impact at all.
Just looking at those who say they are still undecided in the general election, the number bumps up to 50 percent in Clinton's favor if Sanders is on the ticket.
For four of the other possible Democratic vice presidential picks—Booker, Castro, Kain, and Franken—over 60 percent of respondents said the choice would have no impact on their support for Clinton. If Warren is the vice presidential choice, 51 percent said it would have no effect.
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The fierce Wall Street reform advocate and outspoken critic of Republican presumptive nominee Donald Trump is in fact being vetted as a potential running mate for Clinton, the Wall Street Journal reported last week; however, according to the New York Times, "there are ample reasons a Clinton-Warren ticket is unlikely to come to fruition."
Sanders, for his part, has not dropped out of the presidential race, though he said Wednesday, "It doesn’t appear that I'm going to be the nominee." And, in an op-ed published Thursday in the Washington Post, he said that "the 12 million Americans who voted for a political revolution [...] want real change in this country, they want it now and they are prepared to take on the political cowardice and powerful special interests which have prevented that change from happening."
The Monmouth poll also asked about six possible running mates on the Republican ticket, and found that Sarah Palin would be a poor pick for Trump. Forty-two percent of registered voters said they'd be less likely to support the Republican ticket if the real estate mogul were to choose the former Alaska Governor and 2008 vice president nominee as his running mate.