Abrams is a little more circumspect about a recent phone call with Biden. The personal dynamic Biden had with Barack Obama is clearly important to him. So what’s Abrams’s relationship with Biden like? “I can speak for me,” she said, choosing her words carefully as she discussed how much she respects the presumptive Democratic nominee. The ticket didn’t come up, she said. Biden’s campaign confirmed that he called Abrams, but didn’t say more. According to several people familiar with the campaign’s running-mate selection process, Abrams is not currently a likely choice.

“Stacey” has become a one-name celebrity to some Democrats despite losing her 2018 bid for governor. She gave the official Democratic response to President Donald Trump’s State of the Union in January 2019, and when she’s included in events that feature governors, senators and other elected officials, she’s often treated like the headliner. It’s hard to ignore, though, that her most significant job in government to date was being the minority leader of the Georgia House, where Democrats dangle on the edge of a superminority. That’s an especially important factor for the 78-year-old Biden, who, if he wins, would be the oldest person ever elected president.

Read: Stacey Abrams is playing the long game

But Abrams has a case to make. She tripled turnout among Latinos and Asian Americans in the Georgia governor’s race. The 40 percent jump in African American turnout was the highest such bump in state history, she told me. Biden, she said, “is an extraordinary candidate, but I believe that campaigns require a broadening of capacity, simply because one person can’t do everything in a campaign. That’s why you have running mates.”

People have been chattering about her prospects for so long that it’s become an inside joke. At a Bloody Sunday anniversary commemoration in Selma, Alabama, at the beginning of March—when Abrams was given a central place of honor, on the pulpit of the famous Brown Chapel—the Reverend Al Sharpton looked over at her and Biden and joked that he was glad to see “our vice president. I’m talking about Stacey, not you, Joe.” (Biden mouthed, “I know.”) Sharpton is now planning to officially back her as his choice for Biden.

“Stacey’s assets are that she can excite a lot of young people. She proved in Georgia that she can get white and black voters,” Sharpton told me today. “I have not at this point endorsed, but I am very much impressed with her.”

Abrams told me she knows people have questions about her qualifications. Her answer is that she’s “spent the last 20 years thinking about international issues independently and been to 16 countries doing policy work ... as an inquisitive young person and then as a legislator.” For foreign-policy experience, that’s a stretch. Then again, Barack Obama and Mitt Romney both took trips to Europe as presidential candidates to show that they knew how to meet with foreign leaders, and it’s not like Mike Pence was or is known for his globe-trotting worldliness. “I’m the only person I know of that’s in this conversation who has successfully run multimillion-dollar nonprofits, for-profits, and have led teams at the state and the local level,” Abrams added.