Unlike so many previous presidential elections, the 2016 campaign has two strong female candidates: Hillary Clinton, representing for the Democrats, and Carly Fiorina, the female face of the GOP.
But according to a panel discussion at Fortune‘s Most Powerful Women Next Gen Summit in San Francisco on Tuesday, Clinton and Fiorina aren’t the only women who should be on our presidential radar.
One name suggested by the panelists as a potential Commander-in-Chief was clearly well-known to everyone in the room: Facebook COO Sheryl Sandberg.
Alex Wallace, media strategist and CEO of AlexInc, said Sandberg has “positioned herself in a smart way. She has the platform and the recognizable brand” to run for president someday.
Juleanna Glover, a public and governmental affairs consultant, suggested that attendees keep tabs on New York Republican Rep. Elise M. Stefanik. Glover called the congresswoman “brilliant and lively,” saying that she could easily see Stefanik in the Oval Office in 15 or 20 years.
Other names bandied around included Sen. Kirsten Gillibrand (D-NY) and Rhode Island Gov. Gina Raimondo, also a Democrat.
Of course, just because these women may be in a position to run for the nation’s highest office doesn’t mean they’ll choose to do so. The panelists agreed that running for president is an incredible strain. And for women, there’s the added “nightmare” of struggling to appear both likeable and effective.
“If you’re too nice, you’re a wimp,” said Wallace. “If you’re too tough, you’re a bitch. If your hair to fashionable, you’re a fashionista. If it’s too frumpy, you’re Barbara Bush.”
For more about Sheryl Sandberg, watch this Fortune video: