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Joe Biden narrows down his VP list, with Karen Bass emerging as one of several key contenders

(CNN) Joe Biden heads into the weekend weighing the biggest decision of his presidential campaign so far, and people close to the process tell CNN that the former vice president is believed to have now begun to narrow his personal shortlist of potential running mates to a handful of women.

In more than two dozen interviews with CNN in recent days, members of Congress, top Democratic donors, Biden allies and others close to the vice presidential vetting process said California Rep. Karen Bass, the 66-year-old chair of the Congressional Black Caucus, has gained real traction in the late stage of the search. Amid furious last-minute lobbying and speculation about Biden's historic decision, California Sen. Kamala Harris and Susan Rice, Barack Obama's former national security adviser, are also believed to be among the most serious contenders.

The search continues to be conducted under extreme secrecy, with even many top campaign advisers in the dark about the vetting process. Several additional women have also gone through extensive examination by the Biden team, including Massachusetts Sen. Elizabeth Warren, Florida Rep. Val Demings and Illinois Sen. Tammy Duckworth. Others, including Atlanta Mayor Keisha Lance Bottoms, Michigan Gov. Gretchen Whitmer and New Mexico Gov. Michelle Lujan Grisham have also received various levels of scrutiny by the vetting team.

Biden's team has yet to tell any of the women they've considered in earnest for the vice presidential role that they are officially out of the running, people familiar with the process said, with one source saying 11 women are still formally being considered.

Bass' new emergence as one of the top contenders has been propelled by intensive lobbying on her behalf by some of her colleagues in the House including influential California Democrats and top donors. Her star has risen after Speaker Nancy Pelosi recommended weeks ago that Bass should not be overlooked.

They've reached out to members of Biden's inner circle in recent weeks, making an impassioned case for why the congresswoman should not be overlooked in the search process. Her backers have painted her as a universally liked and respected member of the House, a team player with experience working with Republicans and leading a state legislature, an African-American woman with a compelling biography rooted in humble beginnings and notably, a safe political choice who would not rock the boat.

"I think Karen has been under counted since Day One," said Steve Westly, the former California state controller and major Biden fundraiser, who said he is glad to see both Bass and Harris on Biden's shortlist.

"Everybody likes Karen Bass. People are scratching their heads saying, who is this woman?" he said. "When you've been speaker of the legislature for a state that's twice the population of New York and the world's fifth biggest economy, you know how to manage media, you understand the economy. I think she is stronger than people think."

Pelosi, who is close to several of the contenders, does not have a preferred candidate in the search, aides insist.

Another unmistakable dynamic that has emerged in recent days: an intensive effort by some Biden allies to torpedo Harris' chances of being chosen.

Even as Biden has publicly praised Harris in recent months, some of his supporters -- both in private and public -- have continued to raise questions through the press, sometimes using sexist language, about whether Harris would be a trustworthy team player, often bringing up Harris' famous attack on Biden in a Democratic primary debate over the issue of busing.

One Democratic aide with knowledge of the search process offered this blunt observation: "Biden allies are laying the groundwork for the vice president to have a reason to not choose her."

In multiple media reports, Biden allies have attacked Harris' motives. Florida donor John Morgan lamented that Harris "would be running for president the day of the inauguration. For me, loyalty and friendship should mean something." Chris Dodd, a member of Biden's VP vetting team, reportedly complained to a donor that Harris showed "no remorse" when asked about her famous clash with Biden on the debate stage.

Former Pennsylvania Gov. and Biden supporter Ed Rendell, who said he currently does not have a favorite in the search for a running mate, said in an interview that Bass is seen as a "very safe choice" in a way that Harris simply is not.

"Kamala can rub some people the wrong way. Karen Bass is not likely to do that," Rendell said. "The number one rule for picking the VP? Do no harm."

Biden clearly came prepared to defend Harris at a press conference on Tuesday in Wilmington, Delaware, with a photograph of a notecard listing these bullet points under Harris' name: "Do not hold grudges." "Campaigned with me & Jill." "Talented." "Great help to campaign." "Great respect for her."

The recent attacks on Harris have prompted cries of sexism.

"This isn't about whining that we're not being treated fairly, although I would argue these women are not," said Karen Finney, a top aide to Hillary Clinton's 2016 campaign. "We know that it's an old trope to say that you can't trust an ambitious woman."

Harris herself told women on a Black Girls Lead 2020 conference stream Friday, "There will be a resistance to your ambition, there will be people who say to you 'you are out of your lane,' " addressing the attacks on her trustworthiness and ambition for the first time this week.

"They are burdened by only having the capacity to see what has always been instead of what can be. But don't you let that burden you," she said, adding that she's experienced it her whole career.

The Biden campaign has largely declined to publicly engage the criticism leveled against Harris until this week, when campaign manager Jen O'Malley Dillon responded to a report that Harris was seen by some as too ambitious.

"Ambitious women make history, change the world, and win," Dillon wrote on Twitter. "Our campaign is full of ambitious women going all out for Joe Biden. He will make this decision, and this is clear: whoever he chooses from the very qualified options to help him win & unite the country, she'll be one too."

One reason Harris has been under fire is that she has long been viewed as a favorite to be Biden's running mate. Her supporters point to the that she was already vetted on the national stage as a presidential candidate and unlikely to surprise the campaign with any last-minute unknowns. While her 2020 campaign ended well before the Iowa caucuses, Harris' backers maintain that she gained a loyal following while running for the White House, and that she would make history as the country's first Black and Asian vice-presidential candidate.

Meanwhile, Rice's emergence as a serious contender has surprised some in the Biden world, given her limited campaign experience. But her close allies point to her governing credentials from her time in the executive branch and her deep foreign policy background at a time of global turmoil. They also say Biden's years-long working relationship with Rice is not to be underestimated, particularly given how he has emphasized wanting a partner who is "simpatico with me."

"If there ever was a time to pick someone without campaign experience, this would be the year," a Cabinet member from the Obama administration, who knows Rice well, told CNN. "Susan would be the best governing partner."

With the months of intensive vetting now drawing to a close, the final decision is left to Biden and his wife, Jill, who has emerged as one of his closest advisers in the process. She has held virtual campaign events with nearly all of the potential candidates, but has not participated in any of the interviews conducted by the search committee, according to people with knowledge of the process. The Biden campaign has also started building out the team that will staff the future vice presidential pick, a source close to the campaign said, but would not detail who will be involved.

When Biden told reporters earlier this week that he would choose a running mate in the first week of August, two aides told CNN that the timing of an announcement was more likely to be pushed back until the week of August 10. But Biden's advisers gave him a deadline of next week to make up his mind, a person familiar with the process said.

Biden enters the final stretch of deliberations as the country confronts a dire public health crisis and a economic recession. President Donald Trump's approval rating has taken a serious hit over his handling of the coronavirus pandemic -- a reality that close allies say should offer Biden the room to choose a running mate without weighing as much as he might in any other election cycle the political and electoral advantages that a specific running mate could offer.

"They don't need to swing for the fences; they don't need it to be a distraction. They don't need to go with someone that isn't tested or someone who's flashy or random," one Biden supporter in close touch with his inner circle said.

"If he's decided, he hasn't told anyone," a longtime friend of Biden told CNN. "But knowing him, he will not make a final decision until the very last moment."

This story has been updated with comments Kamala Harris made Friday and additional reporting on Nancy Pelosi's approach to the VP selection.

CNN's Arlette Saenz and Annie Grayer contributed to this report.