The word unprecedented has been used a lot throughout this pandemic, but when Hannan added up each piece that needed to fall into place for the program to be a success, there's no better word.

For starters, the American healthcare system presented plenty of challenges. "Our healthcare system is a private sector system. It's not government-run and you're introducing a government-supplied product to it," said Hannan. "This is just completely new, completely unprecedented."

Then there are the smaller details. Hannan said if you simply think of the amount of vaccine that sites are receiving -- one shipment of the Pfizer/BioNTech vaccine has more than one thousand doses -- that in itself poses a challenge. It contrasts with the usual vaccine programs for children when doses are ordered in increments of 10.

Add in the fact that there are three different authorized vaccines, with three different dosing regimens and things get even more complicated.

It's the little things

Hannan said one of the biggest factors that has contributed to the US success is the simple fact that the vaccine supply has increased.

Now, more than 100 million doses of Pfizer/BioNTech and Moderna's vaccines have been delivered to states and each company has promised hundreds of millions more by the summer.

Johnson & Johnson has been more of a slow starter, but the company says it's confident it can deliver 100 million doses by May.

But manufacturers have also tried to drill down on the little details to help smooth out vaccination efforts.

Pfizer was able to come up with several syringe combinations to make sure the full six doses were extracted, automatically increasing the supply.

Pfizer has also worked to get approval for its vaccine to be stored at less cold temperatures for a two-week period. "This alternative temperature for transportation and storage of the undiluted vials is significant and allows the vials to be transported and stored under more flexible conditions," Dr. Peter Marks, director of the FDA's Center for Biologics Evaluation and Research.

And later this year, Pfizer plans to submit a new formulation of its vaccine that would not require the addition of a diluent, removing one step in the process for those administering vaccines.

No silver bullet

While there have been examples of states improving their vaccination efforts, Hannan says there has not been a single strategy that has worked across the board.

"States are set up differently. Some of them are centralized, some of them are not, you know, more rural," says Hannan. "I do think that demand is different in different states."

That difference can impact how states may view vaccination success.

For example, a CNN analysis determined that New York and North Dakota will be the first to vaccinate all willing adults, but this is for very different reasons.

New York has one of the fastest rollouts in the country, vaccinating almost 1% of its population per day, but it needs to move that fast since demand is high. At least 85% of adults in the state say they've been vaccinated or plan to.

North Dakota is vaccinating more slowly, but it has a higher rate of vaccine hesitancy. Around 68% of adults in that state say they've been vaccinated or plan to, meaning the end goal is going to be lower.

Go big or go home

In the beginning, healthcare workers and long-term care residents were the priority, a strategy Hannan agrees with, but she also said this caused things to move more slowly at first because that strategy was more methodical.

"In a lot of respects, it was slower than we thought. It was slower than anybody wanted. Obviously, we're in a pandemic. But I do think we did very well. And we certainly learned from our mistakes."

One of the lessons that has come out of that has been the importance of mass vaccination sites. On Monday, the Biden administration announced the opening of yet another one of these sites in Oregon. The administration says it will have opened 36 mass vaccination sites by the end of next week and will have the combined capacity to administer 124,000 doses a day.

There also have been improvements in the scheduling tools, Hannan said.

"Every week, there's just been an improvement to the scheduling systems. There's obviously been a lot of hiccups, I think many of us have had to deal with the chaos of trying to find an appointment. But little things like that have made it easier."

Eligibility for everyone

As the Biden administration seeks to open eligibility to everyone 16 and up by the end of the month, Hannan says it will be important to maintain momentum.

"If you're not staying ahead of that, you could snap your fingers and all of a sudden, you've got people waiting and you haven't gotten them scheduled," Hannan said.

But even with eligibility being thrown wide open, Dr. Scott Gottlieb, former commissioner of the US Food and Drug Administration and a current board member at Pfizer, said the US is approaching a point where supply will outweigh demand in a matter of weeks.

"I think a lot of states are going to see themselves with excess supply and excess appointments, so it's going to be a shame to look back, and in retrospect realize, that we probably should have put more vaccine into some of these hotspots to snuff them out earlier," he said on "Face the Nation" Sunday.

While Hannan says the US has found great success vaccinating those who want it, the biggest challenge moving forward will be reaching the parts of the population that may be hesitant or have simply not made an effort to get vaccinated. And that will take an entirely different strategy.

"We're going to have to do everything that we can. We're going to have to use community leaders, church leaders. We're going to have to take the vaccine to people, we're going to have to get it to private physicians."