(AP) — The U.S. ramped up COVID-19 vaccinations in the past few days after a slower-than-expected start, bringing the number of shots dispensed to about 4 million, government health officials said Sunday.

The U.S. death toll has climbed past 350,000, the most of any country, according to data compiled by Johns Hopkins University, while more than 20 million people nationwide have been infected. States have reported record numbers of cases over the past few days, and funeral homes in Southern California are being inundated with bodies.

Los Angeles Mayor Eric Garcetti said the pandemic is getting worse in his city as the virus spreads rapidly within households and people let their guard down. “This is a virus that preys off of our weakness, preys off of our exhaustion,” he said.

Experts believe that the real numbers of U.S. deaths and infections are much higher and that many cases were overlooked, in part because of insufficient testing.

Dr. Anthony Fauci, the nation’s top infectious-disease expert, said he has seen “some little glimmer of hope” after 1.5 million doses were administered in the previous 72 hours, or an average of about 500,000 per day, a marked increase in vaccinations. He said that brings the total to about 4 million. 

He acknowledged the U.S. fell short of its goal of having 20 million doses shipped and distributed by the end of December. 

“There have been a couple of glitches. That’s understandable,” Fauci said. “We are not where we want to be, there’s no doubt about that.”

But he expressed optimism that the momentum will pick up by mid-January and that ultimately the U.S. will be vaccinating 1 million people a day. Biden’s “goal of vaccinating 100 million people in the first 100 days is a realistic goal,” Fauci said.

Dr. Moncef Slaoui, the chief science adviser to Operation Warp Speed, the government’s vaccine development and distribution effort, told CBS that 17.5 million doses have been shipped. About 13 million of those have been distributed to clinics, hospitals and other places where they will be administered, according to Fauci.

The 20 million-dose goal hasn’t been reached because local health departments and medical facilities had to stay focused on testing to handle a surge in cases, U.S. Surgeon General Jerome Adams said. And the holiday season meant health workers were taking time off, he said.

On Sunday morning, Trump falsely tweeted that the outbreak has been “far exaggerated” because of the Centers for Disease Control and Prevention’s “ridiculous” methodology. He complained, too, that Fauci has been credited by the news media with doing “an incredible job” when Fauci “works for me and the Trump Administration, and I am in no way given any credit for my work.” 

Fauci and others are warning that an additional increase is likely because of holiday gatherings and the cold weather keeping people indoors.

“It could and likely will get worse in the next couple of weeks, or at least maintain this very terribly high level of infections and deaths that we’re seeing,” Fauci said. 

The worries extend overseas, where British Prime Minister Boris Johnson said more onerous lockdown restrictions in England are likely as a variant of the coronavirus has pushed infection rates to their highest levels on record. More than 50,000 new infections have been reported daily over the past six days. 

Scientists have said the variant is up to 70% more contagious. While Fauci said the U.S. needs to do its own study, he sought to reassure viewers that British researchers believe that the mutated version is no deadlier or more likely to make people sicker and that vaccines are effective against it. 

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Associated Press writers worldwide contributed to this report.