The Supreme Court shoots down a Republican challenge in Pennsylvania as states pass a critical deadline. It’s Wednesday, and this is your politics tip sheet. Sign up here to get On Politics in your inbox every weekday.

Where things stand

• With a flick of the wrist, the Supreme Court cut down a Republican attempt to have President Trump’s loss in Pennsylvania overturned. In a one-sentence order yesterday, with no justices publicly dissenting, the court refused to hear a challenge to the use of mail ballots in Pennsylvania.

• It was a stark rejection of Trump’s attempts to dispute the election, from a court that includes three justices he appointed and upon which he had pinned his postelection hopes.

• The country yesterday reached what elections experts refer to as the “safe harbor” deadline, generally accepted to be the date by which all state-level election challenges — such as recounts and audits — must be completed. State courts are likely to throw out any new lawsuit challenging the election after this deadline. Whether he openly admits it or not, Trump’s attempt to overturn the election appears to be nearing its inevitable end.

• The White House dived back into stimulus negotiations with congressional Democrats yesterday, offering a $916 billion proposal that Steven Mnuchin, the Treasury secretary, shared with Nancy Pelosi, the House speaker, and Mitch McConnell, the Senate majority leader. The deal would include one-time cash payments to Americans and aid to state, local and tribal governments.

• The proposal also includes a provision granting broad legal immunities to employers that have kept on workers during the pandemic. That’s a key demand of Republicans, but it’s a line that Democratic leaders have said they’re unwilling to cross.

• McConnell indicated early yesterday that he would drop his demand for the sweeping liability shield if Democrats would give up on seeking billions of dollars in aid for state and local governments. But Democratic leaders quickly dismissed that idea.

• Now that it’s in a lame-duck session, Congress seems uncommonly busy. The House passed a military spending bill yesterday that includes language removing Confederate names from American military bases, something President Trump has vowed to veto.

• This sets up the potential for the first veto override of Trump’s presidency. The bill passed the House with a veto-proof bipartisan majority of 335 to 78, and now heads to the Senate, where it is also expected to receive overwhelming support.

• Congress has successfully passed annual military spending legislation in each of the past 60 years. But the president remains opposed. “I hope House Republicans will vote against the very weak National Defense Authorization Act (NDAA), which I will VETO,” Trump wrote on Twitter.

• Joe Biden will pick Representative Marcia Fudge, Democrat of Ohio, to serve as secretary of housing and urban development, and he wants to bring Tom Vilsack back to his old job as agriculture secretary, according to people familiar with the presidential transition process.

• Meanwhile, retired Gen. Lloyd Austin, whom Biden intends to name as defense secretary, is running into bipartisan resistance amid concerns over choosing another former commander to run the Pentagon. The recent trend has bucked the longtime tradition of civilian control over the military.

• Austin, who would become the country’s first Black defense secretary, would need to receive a waiver from Congress because he retired from the service fewer than seven years ago. Congress granted a waiver to Jim Mattis four years ago to serve as Trump’s first defense secretary.

• But adding to the concerns over Austin are his ties to Raytheon, a defense contracting company that makes billions of dollars selling weapons and military equipment to the United States and other countries, leading to what critics have called a conflict of interest.

• Biden formally unveiled the core team of health officials that will guide his response to the pandemic, appearing in Wilmington, Del., to announce an ambitious plan to get “at least 100 million Covid vaccine shots into the arms of the American people” in his first 100 days as president.

• The pledge represents at least some risk for Biden, as fulfilling it will require no hiccups in manufacturing or distributing the vaccine and a willingness by Americans to be vaccinated.

• As he spoke, Biden was flanked by members of his team, with some joining via video. They included Dr. Anthony Fauci, who will serve as Biden’s top medical adviser while continuing in his role as the country’s top infectious disease expert, and Dr. Rochelle Walensky, who will become the director of the Centers for Disease Control and Prevention.

• They both delivered speeches, as did Xavier Becerra, Biden’s nominee for secretary of health and human services, and Dr. Marcella Nunez-Smith of Yale University Medical School, who will head a new “Covid-19 equity task force.” The virus’s effects have been disproportionately concentrated in communities of color, and Nunez-Smith spoke of “centering equity in our response to this pandemic, and not as a secondary concern, not as a box to check, but as a shared value.”

• Yesterday Britain became the first country to begin administering the Pfizer-BioNTech coronavirus vaccine to civilians, the start of a mass vaccination campaign unlike any in recent memory. (And trust that Britain was very British about it, indeed: The second person to receive the vaccine was none other than William Shakespeare, 81, a Warwickshire man who had been hospitalized for several weeks after suffering a stroke.)

• The F.D.A. is expected to approve the vaccine this week, and Trump celebrated the milestone at a “vaccine summit” near the White House. He spoke to a packed, mostly masked crowd of industry officials and members of his administration, declaring the vaccine’s development a “monumental national achievement.”

• Asked why he hadn’t welcomed Biden’s transition team to the summit, Trump repeated his baseless claims that the election had been stolen, and said he still expected to serve another term.

Photo of the day

At his “vaccine summit” yesterday, President Trump signed an executive order meant to prioritize the vaccine for Americans over people in other nations.

How safe is it to bring students back to schools?

A large component of Biden’s message to the country yesterday was his promise to ensure that safely returning children to school would be a “national priority.”

Mayors across the country have wrestled with the question of how to reopen schools, and without a clear national framework, the process has been full of switchbacks and frustration — perhaps nowhere more haltingly and publicly than in New York City.

Many parents are frustrated with the difficulties of juggling working from home and taking care of their children 24/7, but polls throughout the pandemic have shown that they favor caution over quickly sending students back to school. Teachers’ unions, too, have emphasized the need for low infection rates in order for schools to safely hold classes.

Still, as experts have debated the benefits and harms of keeping students in remote learning for months on end, the consensus has shifted. New York’s mayor, Bill de Blasio, elected to bring elementary school and special-needs students back for in-person classes this week.

It’s not going to be a smooth process. The city’s regulations will cause entire classes, if not schools, to close abruptly in cases of infections, and the mayor has offered no guarantee of when he plans to bring back middle and high school students.

But it reflects a growing medical consensus that it is safer for the youngest children to convene amid the pandemic, while there is a higher risk for older grade-school students.

Schools reopened successfully in England in the summer without a spike in cases, a study published yesterday found. But England was not already seeing a surge in infections at that time, as the United States is now, and children aren’t the only people exposed when schools reopen. According to the British study, a majority of the school-related infections that were recorded were among staff members.

Biden said yesterday that he would put a priority on ensuring that educators had access to the vaccine as part of his push to bring students back in person.

On Politics is also available as a newsletter. Sign up here to get it delivered to your inbox.

Is there anything you think we’re missing? Anything you want to see more of? We’d love to hear from you. Email us at onpolitics@nytimes.com.