More than a third of likely voters backing Democrat Hillary Clinton in the latest Bloomberg Politics national poll say she should pick Senator Elizabeth Warren of Massachusetts, a darling of the party's liberal wing, as her running mate.

On the Republican side, almost a third of likely voters supporting Donald Trump say former House Speaker Newt Gingrich would be his best pick. Senator Marco Rubio of Florida, a man the presumptive GOP nominee has often referred to as "Little Marco," is selected by about a quarter of Trump's backers, making him the second most popular pick among seven widely mentioned names.

Warren received support from 35 percent of Clinton's supporters in the poll. Senator Cory Booker of New Jersey and U.S. Secretary of Housing and Urban Development Secretary Julian Castro are the only two other Democratic names to break into double-digits among six tested.

Read the questions and methodology here.

Likely voters of all political stripes are split on whether the U.S. is ready to elect two women as president and vice president, with 46 percent saying yes and 48 percent saying no.

Men and women look at the question differently, and not in a way that might be expected, the poll shows. A majority of men, 55 percent, say the nation is ready to elect two women to the nation's top jobs. It's women who are skeptical, with a majority of 59 percent saying that the nation isn't ready.

While neither presumptive nominee is expected to pick their running mate until closer to next month's national conventions, the parlor-game speculation is already intensifying.

After Gingrich and Rubio, John Kasich is the next most popular choice for a running mate among those backing Trump, with 18 percent selecting the Ohio governor.

In an effort to measure whether other business types have the prominence to ever mount a campaign like Trump's using their ties to commerce as a springboard, Bloomberg Politics polled the popularity of four technology-company leaders who have all had higher national profiles. The results showed that most of them aren't that well known.

The least familiar among the four is Sheryl Sandberg, Facebook's chief operating officer. Almost two-thirds of Americans didn't give an opinion about her, while 20 percent said they viewed her favorably and 15 percent unfavorably.

Mark Zuckerberg, Facebook's CEO, is the best known among those tested, with just 37 percent giving no opinion. He's viewed favorably by 40 percent and unfavorably by 23 percent.

Fifty-five percent of Americans said they don't know enough about Elon Musk, chief executive of Tesla Motors and SpaceX, to form an opinion. Among those that did give one, 37 percent said they view him favorably and 8 percent negatively.

Mark Cuban, a technology entrepreneur and owner of the Dallas Mavericks basketball team, is viewed favorably by 37 percent of Americans and unfavorably by 16 percent. Nearly half, 47 percent, said they didn't know enough about him to form an opinion.

The poll, conducted Friday through Monday, included 1,000 adults and has a margin or error of plus or minus 3.1 percentage points. The questions on vice-presidential candidates were answered by 333 Trump supporters and 332 Clinton supporters and both have a margin of error of plus or minus 5.4 percentage points. The survey was directed by Selzer & Co. of West Des Moines, Iowa.

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