U.S. Ambassador to the United Nations Nikki Haley exits President Donald Trump's Cabinet as the most high-profile female member, potentially putting her back into play as a candidate for a Republican Party struggling to gain traction with female voters.

In her out-of-the-blue announcement Tuesday, Haley, 46, pointedly tried to shut down talk that she would run for any office in 2020, including challenging Trump in his re-election bid.

But that hardly stopped Washington from playing a new round in its favorite parlor game: Who's running for what? President, vice president and U.S. senator were all on the table.