When U.S. Democrats named Hillary Clinton their presidential nominee on Tuesday night, the first time they have chosen a woman, a crowd of Bernie Sanders supporters abandoned the historic moment and walked out of the Wells Fargo Center in protest.

There was another female leader, of another political party, waiting for them and welcoming them with open arms.

"We are in FDR Park," Green Party Leader Jill Stein wrote on Twitter. "Ready to meet up with refugees from DNC tyranny."

They found her across the street from the arena. They surrounded her, joining those who were already outside rallying, and they chanted: "Jill not Hill."

Stein's been all over the city this week, attending various rallies and protests, and making the rounds inside the arena where the world's media outlets are covering the convention. She says she's "overwhelmed" by the positive response she's received.

On social media and in person, Stein is blatantly recruiting Sanders supporters, the ones who are disgruntled with the Democratic National Committee and who count themselves among the "Never Hillary" crowd.

A supporter of the Green Party's Jill Stein holds a sign at a rally in Philadelphia on Monday. (Meagan Fitzpatrick/CBC )

Sanders's rallying cry during his campaign was for a political revolution and now that his bid for the presidency is over, Stein is promising to keep it going.

"Do not give up. The revolution has a home with the Green Party," she told the Vermont senator's voters.

Urges Sanders voters to join her

She is encouraging them to ditch the Democratic Party, an idea known as "DemExit," named after "Brexit," the campaign in favour of Britain leaving the European Union.

"The time for a #DemExit is now. Join us," she wrote this week to Democrats, whose convention got off to a rocky start on Monday thanks to news about hacked and leaked emails from the DNC that disparage Sanders and his campaign.

Stein hasn't been shy about taking digs at Clinton, who on Thursday night will give a speech and accept her party's nomination.

There are Sanders supporters here who refuse to get behind Clinton and will not vote for her. Stein is their Plan B.

On the day Sanders endorsed Clinton earlier this month, Barbara Griffin donated to Stein's campaign.

Cornel West, a high-profile author and activist, poses for pictures with fans at a rally in support of Green Party Leader Jill Stein on Monday. He was originally a Bernie Sanders supporter. (Meagan Fitzpatrick/CBC )

"If he's not going to be on the ticket, I'm voting for Jill," she said at a rally at Philadelphia's city hall on Monday in support of Stein and other causes. "She stands for everything we believe in," said Griffin, who is from Ithaca, N.Y.

Raoul Mallalieu was also there holding a large cloth banner that read: "Sanders Stein 2016" on the front and "Go Green Bernie!" on the back.

Sanders sparks interest in Stein

"We're hoping that the day after this convention is over … he decides to go for the Green Party, or at least all of his supporters do," said Mallalieu, who lives in nearby New Jersey.

Sanders has made it clear he is sticking by Clinton and he's encouraged his supporters to vote for her too, to ensure that Republican presidential nominee Donald Trump is defeated in November. But not all of them are taking his advice.

Mallalieu said he will vote for Stein in November and he credits Sanders "100 per cent" for sparking his interest in her party.

Raoul Maillalieu holds a sign calling for Bernie Sanders and Green Party leader Jill Stein to run together for president and vice-president in November's U.S. election, at a rally in Philadelphia on July 25, 2016. (Meagan Fitzpatrick/CBC )

Vanessa Meraki, another rally attendee, was already active in the Green Party before Sanders came along, but she said Stein is benefiting from the energy Sanders generated with his campaign. He mobilized millions of Americans, many of them younger voters, who enthusiastically answered his call for a political revolution and are who are passionate about keeping the momentum going.

"That energy is looking to go somewhere. So I say, thank goodness for Jill Stein because if not for Jill Stein, who knows what would have happened to that energy for change," said Meraki, who crossed the country from Seattle to Philadelphia to be part of the rallies this week.

She noted how closely aligned Sanders and Stein are on policy issues and some Sanders supporters say that's why they can so easily shift their support to her.

Vote split on the left

Stein proposes cutting spending on the military by at least 50 per cent and closing foreign military bases, which would ensure free college for everyone she says, and she would also cancel all student debt if elected president. She wants single-payer public health insurance, a $15 an hour minimum wage, and environmental protection policies, including a ban on fracking, as part of what she calls a "Green New Deal."

Mike Hughes, a Floridian who worked on Sanders's campaign, said he's disappointed the Vermont senator is supporting Clinton and not Stein.

"Bernie's movement has brought a lot of things to light that she also supports and so it's so easy for us to segue to her campaign," Hughes said while milling about in the crowd of protesters in the sweltering heat.

Some Bernie Sanders supporters, like this woman at a protest march in Philadelphia on Monday, are now carrying the flag for the Green Party. (Meagan Fitzpatrick/CBC News)

Is he worried that Sanders supporters moving to Stein will split the vote on the left and benefit Trump?

"No. We have to vote our conscience," he said.