Trump and his legal team, as part of a continued effort to overturn the results of the 2020 election, are ramping up their apparent pressure campaign on Republican-controlled legislatures in key states to try to appoint pro-Trump electors to overturn election results.

At the end of a more than four-hour bipartisan hearing on the election in Michigan on Wednesday, Trump’s personal attorney Rudy Giuliani directly pleaded with state lawmakers to intervene and appoint Trump electors based on mostly debunked claims of fraud offered without evidence.

“I would never certify an election or have my name associated with anything that was false. Now it is your responsibility to do that. Not the governor, not the secretary of state. You were given that responsibility by our Founding Fathers,” he said, pushing the lawmakers to subvert the popular vote. “You can take that power back any time you want to -- anytime -- you can take it back tonight.”

Giuliani is at the Georgia State Capitol Thursday where the Republican-dominated Senate is holding two hearings on the election, the latest in a string of hearings requested by the Trump team and its allies before state lawmakers -- but not in courtrooms, where witnesses might face penalties for lying under oath.

Trump’s latest lawsuit, too, takes a similar approach -- breaking from those used in nearly three-dozen previous cases filed by Trump's campaign and his supporters, most of which have been rebuffed by judges because they failed to sufficiently document claims of fraud and never actually allege that fraud occurred in the state.

A federal lawsuit filed late Wednesday in Wisconsin says only that the risk of fraud was elevated by measures state officials took due to the global COVID-19 pandemic, such as expanding the use of drop boxes and mail-in ballots. The proposed remedy: throwing the outcome of the state's contest to the Republican-controlled state legislature.

Prior to this case, officials in the state told ABC News that they saw no way the legislature could overturn or invalidate the results of the election without a court ruling.

Only two weeks ago, Trump invited Michigan lawmakers to the White House ahead of the state’s certification deadline.

In Michigan, the legislature is not involved at all in the electoral process, and state law does not allow it to intervene at any point to circumvent the process and appoint their own slate of electors, regardless of the popular vote, but it could seek to intervene under Article II of the Constitution. This unprecedented move is also one that top state lawmakers have not embraced. Instead, they've said they will follow the law and the "normal process."

Anthony Michael Kreis, professor of constitutional law at Georgia State University, said Georgia lawmakers could "theoretically" try to appoint electors through legislation but that it would require calling a special session -- an idea which GOP Gov. Brian Kemp and top lawmakers in the state have previously shot down.

"I think the real goal is to try to delay certification so that the electoral votes don’t count at all, but I don’t think there’s any legal theory to support that. It is all smoke and mirrors," Kreis told ABC News.

-ABC News' Matthew Mosk, Olivia Rubin, Kendall Karson, Quinn Scanlan and Cheyenne Haslett

Gov. Gina Raimondo of Rhode Island, who emerged as a potential selection to lead the Department of Health and Human Services in the incoming Biden administration, said Thursday she will not be the nominee.

“I am not going to be president elect Biden's nominee for HHS Secretary. My focus is right here in Rhode Island as I have said, I'm working 24 seven keeping islanders safe and keeping our economy moving. And I have nothing else to add on that,” Raimondo said at her weekly press conference on COVID-19.

The Harvard, Oxford and Yale-educated official was long been rumored as someone who could enter a Biden administration, after she was vetted as a possible pick for vice president.

Elected as Rhode Island's first female governor in 2014, she was seen ahead of the election as a possible nominee for Treasury or Commerce secretary, given her Wall Street background -- which had also made her a target for progressives hoping to influence Biden's incoming administration.

-ABC News' Luke Barr and Benjamin Siegel

In the aftermath of Attorney General William Barr telling the Associated Press the Justice Department has not found evidence of voter fraud on a scale that could overturn the election, Trump was asked in the Oval Office Thursday whether he still had confidence in Barr -- but didn't directly answer.

"Ask me that in a number of weeks from now," Trump said.

Trump said the Justice Department "should be looking at all of this fraud" -- not just limited to civil issues -- and that Barr "hasn’t looked."

His comments come after Barr met with Trump at the White House following the Tuesday interview, with one source briefed on the meeting describing their interaction as "intense," but not elaborating with any additional details about the content of their discussion.

In the days after Biden was officially projected the winner of the election, Barr issued a memo to federal prosecutors authorizing them "to pursue substantial allegations of voting and vote tabulation irregularities" in the event there are "clear and apparently-credible allegations of irregularities that, if true, could potentially impact the outcome of a federal election in an individual State."

At the same time, Barr urged investigators to be vigilant against "specious, speculative, fanciful or far-fetched claims" that he said "should not be a basis for initiating federal inquiries."

But more than three weeks later, the DOJ and FBI have announced no such investigations relevant to the parameters of Barr's memo as an increasing number of states have moved forward with certifying their vote tabulations.

"Most claims of fraud are very particularized to a particular set of circumstances or actors or conduct," Barr said Tuesday. "They are not systemic allegations. And those have been run down; they are being run down."

The president on Thursday concluded that the election was “fixed” and “rigged” before refusing to answer follow-up questions. He made the comments during a jam-packed, largely maskless Oval Office ceremony in which he awarded the Medal of Freedom to football coach and Trump supporter Lou Holtz.

-ABC News' Ben Gittleson and Alexander Mallin

The Biden transition formally announced Brian Deese as director of the National Economic Council on Thursday.

Deese previously served as a deputy director of the National Economic Council, deputy director of the Office of Management and Budget and senior adviser to former President Barack Obama. He played a role in the auto industry bailout in 2009, working alongside then-Vice President Biden.

“Brian is among the most tested and accomplished public servants in the country -- a trusted voice I can count on to help us end the ongoing economic crisis, build a better economy that deals everybody in, and take on the existential threat of climate change in a way that creates good-paying American jobs,” Biden said in a release announcing the pick.

Larry Kudlow currently serves in the position for the Trump adminstration.

-ABC News' Molly Nagle