WASHINGTON — Swine flu has sickened about 22 million Americans since April and killed nearly 4,000, including 540 children, say startling federal estimates released Thursday.

The figures — a quadrupling of previous death estimates — don't mean swine flu suddenly has worsened, and most cases still don't require a doctor's care. Instead, the numbers are a long-awaited better attempt to quantify the new flu's true toll.

"I am expecting all of these numbers, unfortunately, to continue to rise," said Dr. Anne Schuchat of the Centers for Disease Control and Prevention. "We have a long flu season ahead of us."

And tight supplies of vaccine to combat the illness continue: Not quite 42 million doses are currently available, a few million less than CDC had predicted last week.

A new Associated Press-GfK poll shows nearly one in six parents has gotten at least some of their children vaccinated against swine flu since inoculations began last month. Another 14 percent of parents sought vaccine, but couldn't find any.

Only about 30 percent of children routinely get flu vaccinations during a normal winter. That even this many have gotten vaccinated against the new flu that scientists call the 2009 H1N1 strain despite the shortage suggests CDC's target-the-young message has gotten through.

But three times as many adults have tried and failed to find vaccine for themselves as have succeeded.

"I know they're trying their hardest," Joy McGavin of Pittston, Pa., said of the CDC's vaccine efforts. She hasn't yet found vaccine for her three children despite a persistent hunt — even though she and her youngest child are at extra risk because of chronic illnesses.

"But it is kind of frustrating, being as my children's school already shut down" because of a big outbreak, McGavin said.

And interest among the young adults who also are at high risk is waning fast, found the AP-GfK poll of 1,006 adults nationwide.

Thursday, Schuchat again urged patience in seeking vaccine.

"It's a marathon and not a sprint," she said. "More vaccine is being ordered and delivered and used every day."

Until now, the CDC has conservatively estimated more than 1,000 deaths and "many millions" of new H1N1 infections. The agency was devoting more time to battling the pandemic than to counting it, and earlier figures were based on laboratory-confirmed cases even as doctors largely quit using flu tests months ago — and experts knew that deaths from things like the bacterial pneumonia that often follows flu were being missed.

Thursday's report attempts to calculate the first six months of the new H1N1 strain's spread, from April through mid-October. The CDC said: