Days after the Trump administration urged states to open coronavirus vaccine distribution to wider groups, including those 65 and older, the nation surpassed the 11 million mark in terms of shots distributed.

As of Thursday, the U.S. had seen over 11.1 million shots go into the arms of Americans, still far less, however, than half the doses distributed.

The federal government has shipped over 30.6 million doses to states nationwide, leaving it up to each individual state as to how to allocate and administer the supply. Initially, states were instructed to reserve supply to ensure those who had received the first shot could return for the second dose some three to four weeks later, but the Trump administration has since shifted its policy.

Health and Human Services Secretary Alex Azar said the updated guidance was issued after the government grew confident in vaccine manufacturing and production speed. Since the initial doses were distributed, many states have opened mass vaccination centers, but reports of longer-than-expected wait times and scarce appointments have begun to surface.

In New York, Gov. Andrew Cuomo threatened hefty fines for hospital systems that were not moving quickly enough to distribute supply to health care workers. Earlier this week the state moved to open up distribution to seniors and those with underlying health conditions, and later included essential workers. However, overloaded websites and long wait times for callers are still proving to be a hurdle.

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"Too many challenges so far for ages 75+ to get vaccinated," said Mark Levine, New York City councilmember and Health Committee chair, in a tweet on Monday. "NYC needs: *Easier to navigate scheduling website & more operators on the dial-in scheduling line *Door-to-door vaccination for the homebound *Outreach by medical providers to their 75+ patients to offer vaccination."

Cuomo had warned before the site launched last week that appointments likely wouldn’t become available for the latest group to become eligible until March or early spring.

Elsewhere, such as Texas, which has the second-highest case count in the country, officials are concerned about vaccine supply after opening up mass vaccination sites that are expected to administer as many as 50,000 shots per day. In California, which leads the nation in cases, counties are said to be begging for more supply.

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"We’re not done with our health care workers and we actually don’t have enough vaccine right now to be able to get done more quickly," Los Angeles County Health Director Barbara Ferrer said, according to the Associated Press. "We haven’t heard back from the state about vaccine availability and how it would be distributed."

Santa Clara County public health officials say the county of 2 million people only has enough vaccine to dose people age 75 or older. Officials said they asked the state for 100,000 doses but had received 6,000.

The state has received more than 2.4 million doses but has only used about a third. Lawmakers have asked the state’s governor to expand authorization for who can administer the vaccine to include nursing students, retired medical workers, firefighters and National Guard members with medical training in an effort to speed distribution.

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President-elect Joe Biden is expected to deliver a speech later Thursday detailing a plan to release all doses for states to use at will. He has previously stated a goal of seeing 100 million shots administered during his first 100 days in office.

"This is going to entail coordination at all levels, as well as resources," Dr. Nadine Gracia, executive vice president of the nonpartisan Trust for America’s Health, told the Associated Press. "There is a commitment the (incoming) administration has articulated to address the needs of communities."

The Associated Press contributed to this report.