BOSTON (UPI) — The 2016 presidential vote might not only elect the United States’ first female president, it might also elect the country’s first female vice president.

John Podesta, chairman of Hillary Clinton’s presidential campaign, said Thursday that if the former secretary of state wins the Democratic nomination she might pick a woman to be her running mate — raising the specter of an historic all-female ticket.

Podesta made the statement during an interview with the Boston Globe, which immediately led to speculation that female candidate would be Massachusetts’ junior senator, Elizabeth Warren — a liberal who could assist Clinton in winning back supporters of her primary opponent, Vermont Sen. Bernie Sanders, who has largely challenged Clinton from her left flank.

“We’ll start with a broad list and then begin to narrow it. But there is no question that there will be women on that list,” Podesta said.

Warren has not endorsed Clinton or Sanders in the Democratic primary.

The comments come at a sensitive time in Clinton’s primary campaign. The front-runner has been careful to sidestep questions about whether Sanders should quit the race, given her large lead among pledged delegates to the convention in Philadelphia in July.

Clinton, mindful she risks offending Sanders’ liberal supporters by appearing to push him out of the race, declined again Thursday morning to call on him to give up what has proven to be a durable challenge funded largely by small online donations from liberals and political independents — two groups Clinton will need if she is to form a winning coalition of voters in November.

Podesta’s comments upend much of the conventional logic about what kind of candidate might help Clinton as a running mate in the general election. Other names floated have included Labor Secretary Tom Perez and Housing and Urban Development Secretary Julian Castro, both Hispanics with strong liberal credentials and executive experience running Cabinet departments in the Obama administration. Former Virginia governor and current Sen. Tim Kaine has also been mentioned as a possible vice presidential candidate.

The so-called Veepstates is a favorite Washington parlor game occupying time during the period between the end of voting in June and the convention in July, though it has yet to pick up much steam given the fluid nature of the race on the Republican side, where the top of the ticket may well be the first point of order before running mates are brought into the equation.

Podesta’s comments come two days after Clinton ran up a large victory in her adopted home state of New York, which leaves Sanders a very narrow path to overtaking Clinton in the race for pledged delegates at the GOP convention. Sanders would need to win an overwhelming majority of the remaining delegates to overtake Clinton, then convince party insiders reporting to the convention as superdelegates to support him instead of Clinton.

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