COACHELLA, Calif. — The sun-baked desert valley tucked behind the San Jacinto Mountains is best known for an annual music festival that draws 100,000 fans a day and a series of lush, oasis resort towns where well-heeled snowbirds go to golf, sunbathe and party. But just beyond the turquoise swimming pools of Palm Springs, more than 10,000 farmworkers harvest some of the country’s largest crops of date palms, vegetables and fruits.

EAST HARTFORD, Conn. — With the nation’s coronavirus vaccine supply expected to swell over the next few months, states and cities are rushing to open mass vaccination sites capable of injecting thousands of shots a day into the arms of Americans, an approach the Biden administration has seized on as crucial for reaching herd immunity in a nation of 330 million.

Annette Carlin feels trapped.

Before the pandemic, Ms. Carlin, who is 84, loved to go on walks in Novato, Calif., with her grandchildren and dance at the senior center. Since March, though, she has been stuck indoors. She has been eager to sign up for a vaccine and begin returning to normal life.

But booking an appointment has been a technological nightmare. Ms. Carlin cannot afford to buy a computer, and would not know how to navigate the internet in search of a shot even if she could. While members of her family might be able to help her there, she avoids seeing them as a safety precaution.