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Kate Bedingfield, senior adviser to President-elect Joe Biden's transition team, said that Biden does not feel that President Trump's legal challenges to the 2020 election results pose a threat to his projected victory.

Despite a loss in Pennsylvania, Trump's campaign is pressing forward with a number of cases, and Trump attorney Rudy Giuliani said last week that more lawsuits may be forthcoming.

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“No, he does not have any concern," Bedingfield told "Fox News Sunday," saying that the Trump campaign's cases "have been laughed out of court after court all across the country" and "are getting absolutely no traction."

She also pointed to a recount in Georgia that Republican officials affirmed showed that Biden won the state. While Gov. Brian Kemp did certify the election results, he did call for a sample audit to compare voters’ signatures on mail-in ballots.

Sunday morning, Trump called for the signatures on the ballots to be compared with their envelopes. 

"It's all about the signatures on the envelopes. Why are the Democrats fighting so hard to hide them," Trump tweeted. "We will find massive numbers of fraudulent ballots. The signatures won’t match. Fight hard Republicans. Don't let them destroy the evidence!"

Georgia Secretary of State Brad Raffensperger, however, has said such a comparison would be impossible at this point because the ballots are separated from the outer security envelope during the counting process, according to CBS News.

Bedingfield went on to accuse Trump of trying to "subvert the democratic system," and said his challenges amount to a "PR stunt" and a "sideshow." She then pointed to Giuliani's marathon press conference on Thursday as evidence that "this is not a serious, sophisticated effort."

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During that press conference, Giuliani and attorney Sidney Powell made sweeping allegations of a "centralized" voter fraud plot. He referenced allegations in sworn affidavits that raised questions regarding the vote-counting processes in several jurisdictions but did not illustrate how they were connected as part of an overarching scheme.

Looking ahead, Bedingfield discussed Biden's preparations for taking office in January, stating that the president-elect will announce his first Cabinet selections on Tuesday. She would not go into any more detail regarding who or even how many picks will be announced.

"Everyone will have to just tune in on Tuesday and it will be made known then," she said.

Bedingfield also said that Biden is ready to get to work on negotiations with Republicans over a coronavirus relief bill. While Democrats and Republicans came together to pass multiple packages earlier in the year, their latest efforts have resulted in a months-long impasse, with Democrats seeking a bill worth trillions of dollars, while Republicans have pushed for a more targeted approach.

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When asked if Biden is ready to meet with Senate Majority Leader Mitch McConnell, R-Ky., now before taking office, Bedingfield replied in the affirmative.

"Yes, absolutely, she said.  "Ad we're very hopeful, we're very hopeful that we'll be able to see progress soon on this bill because people all across the country desperately need it."