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Bloomberg Politics polled supporters of both candidates and asked who they thought would be the best pick.
For Trump, former Speaker of the House Newt Gingrich came out on top, with 29 percent support. But he was followed closely by former presidential candidate Sen. Marco Rubio at 24 percent, and that 5-point difference is within the margin of error.
See Trump through the years:
It's important to note that this is just a poll, and opinions change. Just a few months ago, Ben Carson was the people's top pick as Trump's VP.
Americans' pick for Clinton's running mate was a little clearer. Sen. Elizabeth
Warren got the most votes with 35 percent. Gaining about half as much support was Sen. Cory Booker with 17 percent, and then U.S. Secretary of Housing and Urban Development Julian Castro at 12 percent.
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One small problem for the fans of Julian Castro as VP – he doesn't want the job.
And there's also a potential snag for the Warren supporters. If Clinton and Warren were to win, Warren would need to vacate her seat in the U.S. Senate, and the
Republican governor of Massachusetts would choose her replacement.
The final decision for each candidate will likely come much closer to their parties' conventions. Both conventions happen in the second half of July.
See Clinton through the years: