WASHINGTON — The Trump administration’s top health officials outlined an ambitious timetable on Sunday for distributing the first coronavirus vaccinations to as many as 24 million people by mid-January, even as the accelerating toll of the pandemic filled more hospital beds across the United States and prompted new shutdown orders in much of California.

With the coronavirus pandemic surging and initial vaccine supplies limited, the United States faces a hard choice: Should the country’s immunization program focus in the early months on the elderly and people with serious medical conditions, who are dying of the virus at the highest rates, or on essential workers, an expansive category encompassing Americans who have borne the greatest risk of infection?

Health care workers and the frailest of the elderly — residents of long-term-care facilities — will almost certainly get the first shots, under guidelines the Centers for Disease Control and Prevention issued on Thursday. But with vaccination expected to start this month, the debate among federal and state health officials about who goes next, and lobbying from outside groups to be included, is growing more urgent.

It’s a question increasingly guided by concerns over the inequities laid bare by the pandemic, from disproportionately high rates of infection and death among poor people and people of color to disparate access to testing, child care and technology for online schooling.

Lately, in the ongoing conversation about how to defeat the coronavirus, experts have made reference to the “Swiss cheese model” of pandemic defense.

The metaphor is easy enough to grasp: Multiple layers of protection, imagined as cheese slices, block the spread of the new coronavirus, SARS-CoV-2, the virus that causes Covid-19. No one layer is perfect; each has holes, and when the holes align, the risk of infection increases. But several layers combined — social distancing, plus masks, plus hand-washing, plus testing and tracing, plus ventilation, plus government messaging — significantly reduce the overall risk. Vaccination will add one more protective layer.

With coronavirus infections soaring across the nation, federal health officials on Friday urged Americans in the most forceful language yet to take steps to protect themselves — starting with consistent, proper use of masks — and pressed local governments to adopt 10 public health measures deemed necessary to contain the pandemic.

The guidance reflected deep concern at the agency that the pandemic is spiraling further out of control and that many hospitals are reaching a breaking point, potentially disrupting health care across the country.

Agency officials have issued increasingly stark warnings in the waning weeks of the Trump administration, and President-elect Joseph R. Biden Jr. has promised a new national strategy to turn back the virus. On Thursday, Mr. Biden said he would call on Americans to wear facial coverings for 100 days.