Washington — President Biden on Tuesday unveiled new plans to fight the spread of the highly contagious Omicron variant of the coronavirus, saying the government would make 500 million rapid at-home tests freely available to Americans, increase support for hospitals and add testing sites in regions that need additional capacity. Starting in January, Mr. Biden said, Americans will be able to request rapid tests through a website and have them delivered, free of cost. The timing of when those tests will arrive on doorsteps and how they will be delivered is not yet clear. In addition, 1,000 members of the military will be deployed to help staff medical facilities caring for COVID-19 patients. There are also plans to send out additional ventilators and equipment from the national stockpile besides expanding hospital capacity to handle infected patients. In a speech at the White House, Mr. Biden said the government will establish new testing sites and use the Defense Production Act to help manufacture more tests. There will also be pop-up vaccination sites, hundreds of new people to administer the vaccines and new rules that make it easier for pharmacists to work across state lines. Mr. Biden said the current shortage of at-home tests in places across the country where the virus is surging should not be considered a failure, since he didn't think anyone anticipated the new variant would spread so quickly. "No, it's not, because COVID is spreading so rapidly, you notice it just happened almost overnight, just in the last month," the president said, asked if it's a failure that the U.S. doesn't have enough tests for everyone who wants one to get one. "So no, it's not a failure. The alarm bell went off. I don't think anybody anticipated that this was going to be as rapidly spreading as it did." The president appealed directly to the unvaccinated, telling them that they have a duty to their country to get their shots. Mr. Biden gave a nod to the Trump administration, saying that "thanks to the previous administration" and the scientific community, the U.S. was one of the first countries to distribute vaccines. He also encouraged Americans to not be shocked by positive cases of the Omicron variant among the vaccinated, trying to assuage fears that this winter will be as difficult as the last one, before there were vaccines and therapeutics. "There will be positive cases in every office, even in the White House, among the vaccinated, from Omicron," Mr. Biden said. "But these cases are highly unlikely to lead to serious illness." The world is confronting the prospect of a second straight holiday season with COVID-19 as families and friends begin to gather while the variant quickly spreads. Scientists don't yet know whether Omicron causes more serious disease, but they do know that vaccination should offer strong protections against severe illness and death. Mr. Biden has found himself in the delicate position of both alerting the country to the dangers posed by Omicron and reassuring Americans that the vaccines will protect them. White House officials are looking to ease the nation back toward accepting the reality of an endemic virus with far lower stakes for the vaccinated. This has meant setting a difficult balance as cases rise and as deaths and serious illness among the unvaccinated dominate headlines. Underscoring how widespread the virus is, the White House said late Monday that Mr. Biden had been in close contact with a staff member who later tested positive for COVID-19. The staffer spent about 30 minutes around the president on Air Force One on Friday on a trip from Orange, South Carolina, to Philadelphia. The staffer, who was fully vaccinated and boosted, tested positive earlier Monday, press secretary Jen Psaki said. Psaki said Mr. Biden has tested negative twice since Sunday and will test again on Wednesday. Citing guidance from the CDC, Psaki said Mr. Biden didn't need to quarantine and would continue with his regular schedule. Scientists say Omicron spreads even more easily than other coronavirus strains, including Delta. It has already become the dominant strain in the U.S., accounting for nearly three-quarters of new infections last week. Early studies suggest that the vaccinated will need a booster shot to have the best chance at preventing an Omicron infection. Even without the extra dose, however, vaccination should still largely protect people from serious sickness or death. In New York City, nearly 42,600 people citywide tested positive from Wednesday through Saturday — compared with fewer than 35,800 in the entire month of November. The city has never had so many people test positive in such a short period of time since testing became widely available; there's no clear picture of how many people got the virus during the city's first surge in the spring of 2020.