NORTH TEXAS (CBSDFW.COM/AP) — Some state are opening football stadiums, major league parks and convention centers, here in North Texas the fairgrounds in Dallas is the site of the first COVID-19 vaccination hub. The so-called mega-centers are meant to inoculate a larger and more diverse pool of people.

After a frustratingly slow rollout involving primarily health care workers and nursing home residents, states are moving on to the next phase before the first one is complete, making shots available to such groups as senior citizens, teachers, bus drivers, police officers and firefighters.

READ MORE: Many Texas Parents Choosing To Homeschool Amid Continued Concerns Over COVID-19

Similarly, in Britain, where a more contagious variant of the virus is raging out of control and deaths are soaring, seven large-scale vaccination sites opened Monday at such places as a big convention center in London, a racecourse in Surrey and a tennis and soccer complex in Manchester.

Across the U.S., where the outbreak has entered its most lethal phase yet and the death toll has climbed to about 375,000, politicians and health officials have complained over the past several days that too many shots were sitting unused on the shelves because of overly rigid adherence to the federal guidelines that put an estimated 24 million health care workers and nursing home residents at the front of the line.

As of Monday morning, nearly 9 million Americans had received their first shot, or 2.7% of the U.S. population, according to the Centers for Disease Control and Prevention. Experts say as much as 85% of the population will have to be inoculated to achieve “herd immunity” and vanquish the outbreak.

Many states are responding by throwing open the line to others and ramping up the pace of vaccinations, in some cases offering them 24-7.

Arizona, with the highest COVID-19 diagnosis rate in the U.S., planned to dispense shots beginning Monday in a drive-thru, round-the-clock operation at the suburban Phoenix stadium that is home to the NFL’s Arizona Cardinals. Shots are being offered to people 75 and older, teachers, police and firefighters.

In Texas, Dallas County opened a vaccine megasite on Monday at Fair Park. Thousands of people lined up before sunrise hoping to get a shot.

READ MORE: Dallas ISD Stocking Each Campus With COVID-19 Rapid Tests: 'We Are Hoping To Have A Safe Start To School'

“This really is the final frontier in the battle against COVID-19.,” said Mayor Eric Johnson.

Dallas County Judge Clay Jenkins says the location is prepared to vaccinate 120 an hour Monday morning, between 150 and 180 by Monday afternoon and 200 an hour by Tuesday.

So far, 140,000 have registered online in Dallas County, but available doses are limited and the location nowhere near that amount available.

“I’m just trying to stay on top of it before I get it. I haven’t had it yet,” said 72-year-old Robert Thompson as he waited in his car. “I just don’t want to get it.”

In Houston, nearly 4,000 people were vaccinated Saturday at Minute Maid Park, the home of baseball’s Houston Astros.

The slow first stage of the campaign has been blamed in part on inadequate funding and guidance from Washington and a multitude of logistical hurdles at the state and local level that have caused confusion and disorganization.

(© Copyright 2021 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)

MORE NEWS: Massive Backup On I-30 Westbound In Rowlett After Police Chase Ends When Minivan Crashes