With just hours to go until Tuesday's "safe harbor" federal law-mandated deadline for states to certify their election results and next Monday's Electoral College voting coming up, time is running out for Trump to find a way to overturn the results of the presidential election as he’s set out to do.

The president held a rally in Georgia -- his first since losing the election -- to campaign for the upcoming Senate runoffs there, races which will determine whether the GOP maintains control, but instead he spent most of his 101 minutes on stage pushing a whirlwind of unsubstantiated claims that the election was stolen.

Trump directly called on GOP Gov. Brian Kemp to "immediately ask for a special session of the legislature" -- which could theoretically set up the process of allowing lawmakers to appoint new electors who would support Trump over Biden despite Biden winning by nearly 12,000 votes in the state.

But Georgia officials have rejected Trump's call.

Kemp, joined by GOP Lt. Gov. Geoff Duncan, said in a statement late Sunday it would be unconstitutional for the legislature to "retroactively change" the process for choosing presidential electors, saying "doing this in order to select a separate slate of presidential electors is not an option that is allowed under state or federal law."

While Kemp and Duncan, along with GOP Secretary of State Brad Raffensperger and officials in his office, have said the only option in disputing the results is through the courts, pro-Trump efforts have ended in at least 38 defeats to date, with only a single court victory -- in a case in Pennsylvania that was ultimately not consequential.

It all comes as the president’s personal attorney tasked with leading his efforts to overturn the election in court, Rudy Giuliani, who has been traveling the country as part of the president's ongoing efforts to dispute election results, remains hospitalized with COVID-19 at MedStar Georgetown University Hospital in Washington since Sunday. The Arizona legislature has closed for the week "out of an abundance of caution" after Giuliani met with roughly a dozen GOP lawmakers.

As deadlines loom, Trump on Monday presents the presidential Medal of Freedom to wrestling legend Dan Gable at noon and meets with Vice President Mike Pence behind closed doors.

And while Trump administration officials vow that with vaccine on the horizon, life will soon return to normal, the Biden team is sounding alarms on its distribution, saying they still don’t have access to the plan to roll it out.

"We have yet to see any kind of detailed plan," Dr. Celine Gounder, an expert on Biden’s COVID-19 advisory board, told "CBS This Morning" Monday after Biden said the same last week.

Pressing forward with the transition despite Trump's roadblocks, Biden and Vice President-elect Harris will receive the President’s Daily Brief and meet with transition advisors on Monday ahead of personally debuting their new health picks, who will inherit leading the country through the ongoing coronavirus pandemic.

The Biden team has announced co-chairs for the Presidential Inaugural Committee with Democratic Rep. James Clyburn of South Carolina, whose endorsement helped put Biden on a path to victory, at the helm to guide the larger committee as they prepare for the event in 44 days.

"This inauguration will show the country and the world something I have always known: we know Joe, and Joe knows us," Clyburn said in a statement through the Biden transition team.

Rep. Cedric Richmond, D-La., Rep. Lisa Blunt Rochester, D-Del., Los Angeles Mayor Eric Garcetti, and Michigan Gov. Gretchen Whitmer will help lead Biden’s team as co-chairs, along with Clyburn who will serve as chair.

“These leaders reflect the strength, spirit, and diversity of America and have always held a steadfast commitment to restoring the soul of the nation, building back the middle class, and unifying the country,” Biden said in a statement Monday morning.

-ABC News Molly Nagle

President-elect Joe Biden unveiled his health team early Monday morning, a slate of seven experts and officials that will lead his administration's response to the ongoing COVID-19 crisis.

California Attorney General and former Rep. Xavier Beccera is nominated as Secretary of Health and Human Services. If confirmed, he would be the first Latino to lead the department.

Vivek Muthy has been nominated to be U.S. Surgeon General, a role he served in during the Obama administration.

Dr. Rochelle Walensky, a leading expert on virus testing, prevention, and treatment, is nominated to serve as director of the Centers for Disease Control and Prevention.

Dr. Marcella Nunez-Smith, one of the country’s foremost experts on health care disparities, will serve as the COVID-19 equity task force chair.

As Biden said last week, Dr. Anthony Fauci will stay on in his current role as as director of the National Institute of Allergy and Infectious Diseases, and will take on the elevated role of Biden's chief medical adviser on the COVID-19 pandemic.

Jeff Zients will serve as coordinator of the COVID-19 response and counselor to the president, and Natalie Quillian will serve as deputy coordinator of the COVID-19 Response.

“This trusted and accomplished team of leaders will bring the highest level of integrity, scientific rigor, and crisis-management experience to one of the toughest challenges America has ever faced — getting the pandemic under control so that the American people can get back to work, back to their lives, and back to their loved ones," Biden said in a statement announcing the picks.

-ABC News John Verhovek and Molly Nagle

From the technical standpoint of a transition of power, the public opinion of congressional Republicans about whether Biden will take office Jan. 20 matters almost not at all.

From the broader standpoint of democracy and faith in elections, it could not hardly matter more at this moment.

The process that so many Republicans have been saying they want to play out is rather thoroughly exhausted already. The next seven days bring significant deadlines, with Tuesday's congressional "safe harbor" deadline for state election results and next Monday's Electoral College voting the most significant.

His tweets and the 101 minutes Trump spent airing grievances and falsehoods in Georgia Saturday night made clear he will pursue his dangerous fictions right through the end of his presidency. The good of the Republican Party -- and, of course, the good of the country -- are, at best, secondary considerations for the president at this point.

Some Republicans are trying to reframe questions about Biden's legitimacy as president-elect as though they are merely asking questions. Their suggestion is that democracy is threatened if people believe election irregularities have been ignored.

But far from being brushed aside, Trump's claims have been rejected in courthouses and state houses -- including by Republicans who have found themselves targeted by the president.

Ignoring that fact only sows more doubt in election integrity and legitimacy. And continuing to give Trump space to make wildly inaccurate and irresponsible claims will only solidify his hold on a party whose best interests have already begun to diverge from the president's.

-ABC News' Political Director Rick Klein

While the U.S. Supreme Court has twice refused to hear pro-Trump challenges to the 2020 elections, a federal judge in Wisconsin on Saturday joined the chorus of rulings against Trump in his effort to use the courts to invalidate Biden’s victory.

“This Court has allowed plaintiff the chance to make his case and he has lost on the merits,” wrote U.S. District Court Judge Brett H. Ludwig, a Trump appointee. Ludwig noted that the president had asked “that the Rule of Law be followed,” and he declared in response: “It has been.”

The ruling comes just one day after the U.S. Supreme Court refused to consider an election challenge brought by the Texas attorney general contesting the way elections were run in four states, including Wisconsin. Trump had called that case “the big one,” because he thought it held the best hopes for him of re-litigating the 2020 contest in court.

This latest ruling marks nearly 50 losses for the president  in cases brought by him and his supporters since election day. In Wisconsin, where Biden won by more than 20,000 votes, Trump asked for 221,000 absentee and mail-in ballots to be excluded on the grounds they were collected in ways not laid out by the state legislature. And the president argued that the legislature should be afforded the chance to select an alternate slate of electors.

Ludwig’s 23-page opinion gave wide latitude to Trump -- finding that the president had standing to file his election challenge and was not too late to raise his concerns about the way the election was conducted. But the outcome of the case was the same as rulings in other battleground states -- that Biden’s victory was attained legally and should not be thrown to a legislature to upend.

The president, Ludwig wrote, “has not proved” that state election officials violated his rights. “To the contrary, the record shows Wisconsin’s Presidential Electors are being determined in the very manner directed by the Legislature, as required by Article II, Section 1 of the Constitution.”

Ludwig further noted that if he followed the demands set out in Trump’s lawsuit, “any disappointed loser in a Presidential election, able to hire a team of clever lawyers, could flag claimed deviations from the election rules and cast doubt on the election results. This would risk turning every Presidential election into a federal court lawsuit over the Electors Clause.”

The Trump campaign has not yet responded to requests for comment.

At the moment the federal ruling was handed down, the Wisconsin Supreme Court was hearing arguments on a separate challenge to a recount of votes in the state, which had failed in a lower court.

-ABC News' Matthew Mosk and Alex Hosenball