By Patricia Sellers
September 18, 2015

Sen. Claire McCaskill (D-MO) doesn’t want Carly Fiorina to be president, but she predicts that the former Hewlett-Packard (HPQ) CEO will be the nominee for vice president on the Republican ticket.

Thursday evening at an event in New York City hosted by TIME and Real Simple (Fortune’s sister publications at Time Inc. (TIME)), McCaskill said: “I would be surprised if [Fiorina] were not selected to be the VP in a campaign where Hillary Clinton is the nominee.”

The U.S. senator from Missouri, during an interview with TIME Managing Editor Nancy Gibbs, was responding to a question that I asked from the audience: “Regarding Carly Fiorina, is the question ‘Is she warm enough?’ a fair question? Is she warm enough? And do you think she has a viable chance of being the Republican vice-presidential nominee?”

McCaskill, who is publicly backing Hillary Clinton in the presidential race, suggests that Fiorina’s warmth—or lack of it—does matter, and if she wants a viable shot at the White House, she needs to be more likable. “Being likable is not something in presidential politics that’s unique to women. Personality matters,” McCaskill said.

But no question, striking the right balance between strength and vulnerability is a particular challenge for women. A former courtroom prosecutor, McCaskill said that she has always struggled to tame her own tendency to come across as too tough. “When you’re a good debater and a woman, it’s important that you smile and be likable,” the senator said, not wanting to give Fiorina any free advice. But she did: “In every debate I’ve done, the big word I write on my pad is ‘Smile.’ And I circle it. Because I get so intense, I forget to be warm and friendly. All candidates need to be warm and friendly.”

Executive coach Mary Civiello, who analyzed the debate performances of the Republican candidates for Fortune, agrees. She praised Fiorina for her commanding demeanor Wednesday at the Ronald Reagan Presidential Library but noted that in aiming to prove that she won’t roll over for Trump or anyone else, Fiorina came across tough—perhaps too tough. “Fiorina was so focused on showing strength that she lost the chance to show what leaders—both men and women—often miss: a winning smile,” Civiello says.

Fiorina’s chances of leading the GOP ticket are slim not only because of her likability but also, her record at the helm of HP and her own flawed assessment of it—as Fortune’s Steve Gandel smartly detailed in a story on Thursday. He notes that HP stock fell 45%—significantly more than the overall market and the company’s major competitors—during her 1999-2005 tenure that ended with the board firing her. And while Fiorina is correct that she doubled the size of HP, mainly by acquiring Compaq, her claim that “we quadrupled its topline growth rate, we quadrupled its cash flow, we tripled its rate of innovation” doesn’t hold up, according to Fortune‘s calculations.

That said, Fiorina is smart and charismatic and has a real shot at being a VP contender. In these coming months, watch for her to start playing up her softer side—as Clinton has done to try to reverse her slide in the polls. If the presidential race has Clinton as the Democratic nominee, Fiorina may well be the GOP’s female antidote, paired with a candidate named Jeb or Marco or…just not Donald.

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