WASHINGTON (AP) — Health and Human Services Secretary Kathleen Sebelius said Monday the swine flu vaccine "is coming out the door as fast as it comes off the production line." But at the same time, she acknowledged delays in getting a sufficient supply for all those demanding it. "We were relying on the manufacturers to give us their numbers and as soon as we got numbers we put them out to the public. It does appear now that those numbers were overly rosy," Sebelius said in one interview. "We do have a vaccine that works," she said. Sebelius said the immune response is working faster than officials anticipated. Appearing Monday morning on nationally broadcast news shows, she said officials now have a supply of about 16.5 million doses of the vaccine, while conceding that's millions of doses below the amount needed. Sebelius said she couldn't predict just how widespread the virus will be. Roughly a thousand people have died from it so far in the United States. But she also said officials do not believe there is yet any cause to close down schools and cease other daily activities. President Barack Obama declared a health emergency over the weekend to give hospitals and health professionals more leeway from federal regulations to respond to the illness. And on Sunday, Senate Republican Leader Mitch McConnell of Kentucky said Congress would be happy to provide additional support and money on a bipartisan basis, if the need arises. Said Sebelius: "If we had found the virus a little earlier we could have started a little earlier." Asked what advice she would give to people who have waited futilely in line for shots, the secretary replied, "I want them to come back." "I hope that people aren't discouraged," she said. "I know it's frustrating to wait in line and particularly if you end up with no vaccine. We wish this could have been smoother, that we had a larger supply. We knew it would come in waves." Sebelius sought to assure people that eventually there will be enough supplies "for everyone." Dr. Anne Schuchat, who heads the Immunization and Respiratory Diseases Division of the Centers for Disease Control and Prevention, said it's hard to predict how long the H1N1 wave will continue, so even getting vaccinated a few months from now — when vaccine supplies are more plentiful — won't be too late. "It wouldn't be too late," she said. "We don't know how long this increase will go on. ... We might see another wave after the first of the year. I think it's important for people to take steps to protect themselves." Sebelius appeared on ABC's "Good Morning America," CBS's "The Early Show" and NBC's "Today" show. Schuchat was interviewed on CNN.