But don't try to line up an appointment just yet: Only as many as 7 million doses of vaccine are expected by week's end. Divided up, that makes for such small initial shipments that most states are reserving early vaccine for doctors and other front-line health workers who already are being sneezed on by flu sufferers.
"I needed that protection," said Dr. John Eshun, a gastroenterologist who was among the first in line for vaccine at Le Bonheur Children's Hospital in Memphis, Tenn. More than 5,500 kids with flulike illness have sought emergency care at that hospital since Aug. 1.
In Indianapolis, health workers made jokes as they waited to have FluMist - the nasal-spray vaccine that, packed in white coolers, was the first shipped - squirted into each nostril while TV cameras rolled.
"It's manufactured the same way as the seasonal flu vaccine, and I never get the flu," said Jennifer McFarland, 30, an Indianapolis paramedic who swears by her annual vaccination and this year will need two - one to protect against swine flu and the other to protect against regular winter flu.
Vaccinations against H1N1 flu won't gear up in earnest until mid-October, when at least 40 million doses will have rolled out, with more coming each week. Even then, first doses are supposed to be for the people at highest risk of catching swine flu. Arkansas earmarked its first shipment, expected Tuesday, for in-school vaccinations. Pennsylvania, too, will send early shipments to school-age kids in parts of the state where H1N1 flu already is active.
But this is uncharted territory. You really can't plan too far ahead to say, "I'll schedule my swine flu shot on Oct. 16 at Clinic X." Only as shipments start arriving will local doctors, clinics, school vaccination programs and drugstores get word that their doses are coming and how much. Each state health department decides that.
Some primary care doctors say they have little information when it comes to the government's plan for immunizing more than half the population, CBS News correspondent Dr. Jennifer Ashton reports. They also say they've been inundated with phone calls from patients and parents seeking to get the new vaccine.
Meanwhile, some physicians are still trying to figure out how to administer a large number of doses quickly - in small offices and with limited staff - while dealing with other illnesses, Ashton reports.
"Take a deep breath, be patient, wait a couple of days, make another phone call and cut everyone a little slack because it's a little hectic out there, folks," says Dr. William Schaffner, a flu vaccine specialist at Vanderbilt University.
And keep track of which vaccine you've gotten: Recipients of the H1N1 flu vaccine are being given "vaccination record" cards to help. Seasonal vaccine is widely available now, even through workplaces, but the lower-risk general public may not get access to the swine flu vaccine until November.
H1N1 Flu Information on the Web:
CBSNews.com Special Report: H1N1
CDC Flu Advice
CDC Flu Questions and Answers
Here's what you need to know:
Q: Why not wait to start until there's enough for everybody instead of the confusing here-and-there vaccinations?
A: Even though Sunday was the official start of flu season, this H1N1 wasn't heeding the calendar - it's already causing illness in nearly every state. That means getting vaccine to the people at highest risk is a race. So each week, states will distribute however much they have on hand.
Q: If factories are still racing vaccine out the door, how can I be sure it's safe?
A: The Food and Drug Administration clears batches of vaccine before they're released. The H1N1 vaccine is made in the same way as the regular winter flu vaccine that is used with very few, minor side effects by nearly 100 million Americans a year. There's no biological reason the H1N1 vaccine should react any differently, and no red flags have appeared in studies of several thousand people.
"What I want people to know is that no corners have been cut at all," said Dr. Anne Schuchat of the Centers for Disease Control and Prevention.
In Indianapolis Monday, Marion County Health Department director Dr. Virginia Caine was even more blunt: "Its safe. It's not an experimental vaccine," she said as she held up a dose headed to area hospitals.
Q: Why is the nasal-spray vaccine arriving before the shots, and can I use either one?
A: They're considered equally effective, but FluMist finished brewing sooner. There is an important difference, though. Flu shots, made of killed flu virus, are for anyone without an egg allergy. FluMist, besides the egg issue, is only for use in healthy people ages 2 to 49 - no pregnancy or underlying conditions. It's made of live but weakened flu virus. So some people on the first-in-line list for the new H1N1 vaccine aren't eligible for FluMist.
Q: Who's first in line?
A: Pregnant women; the young, ages 6 months through 24 years; people younger than 64 who have conditions such as asthma or diabetes that increase the risk of complications from flu; health workers and caregivers of newborns.
Q: I thought flu was most dangerous to people 65 and older.
A: Regular winter flu is most dangerous to older adults, but the new H1N1 is predominantly striking the young.
Q: How many shots, or squirts, will I need?
A: Most people will need one dose each of the swine flu vaccine and the regular winter flu vaccine. But health authorities believe children under 10 will need two doses of the swine flu vaccine, about three weeks apart. And some very young children getting their first regular flu vaccination will need two doses of it, too, for a total a four inoculations.
Q: If the new H1N1 is the only flu strain making people sick now, why do I need the regular shot?
A: Health authorities expect regular flu strains to start circulating, too, as it gets colder; seasonal flu typically peaks in January.
Q: Can I get both types of vaccine at the same visit?
A: If you're lucky enough to find a provider who has both at the same time, a jab in each arm is OK, or a jab of one and a squirt of the other. If you opt for the FluMist version of each vaccine, however, you're supposed to wait three to four weeks between squirts.
Q: What will it cost?
A: The H1N1 vaccine itself is free because the government bought it with your tax dollars. But providers can charge a fee for administering it, usually about $20. Regular flu shots tend to cost up to $35.