Gov. Gavin Newsom and California’s top health official love the sound of President Joe Biden’s plan to make all adults eligible for coronavirus vaccines by May 1.

But they’re stopping short of agreeing that California will throw the vaccination doors open to everyone just seven weeks from Saturday.

Instead, responses to Biden’s Thursday evening speech from Newsom and Dr. Mark Ghaly, secretary of the state’s Health and Human Services Agency, have put the onus back on the federal government to follow through on that pledge.

“We share the president’s commitment to ensuring all adults who want a vaccine can get one,” Newsom said in a statement Thursday. “We look forward to learning more about the president’s plan and working together to make this important goal a reality.”

Asked during a briefing Friday about Biden’s vision of marking “independence” from COVID-19 by celebrating the Fourth of July with backyard gatherings, Ghaly said, “We’re not circling a date quite yet — but we’re ready for something around that time if all of these different pieces come together as we all hope.”

A key piece, according to Ghaly, will be providing California with far more COVID vaccines.

The state now administers 200,000 to 240,000 shots per day, Ghaly said, but will need to give out perhaps twice that many — 350,000 to 400,000 each day — to get closer to Biden’s goal.

“Our job in the state is to be ready for whatever the federal government (and) the manufacturers can send us, and that is what we’re working hard to be ready for,” Ghaly said.

Tight supplies have meant those who are eligible to get shots now — including people 65 and older, food and agriculture workers, educators and healthcare workers — sometimes struggle to book appointments, while some Bay Area providers have had to cancel appointments or stop scheduling new ones.

And while vaccine supplies are not expected to dramatically increase in the coming weeks, California will broaden its eligibility pool by more than 4 million people on Monday, allowing residents who have certain serious medical conditions, as well as public transportation and airport workers, among others, to get shots.

State officials have said they believe substantially more doses will begin arriving in April, as manufacturing of the single-shot Johnson & Johnson vaccine ramps up, adding to the shots from Pfizer and Moderna.

California’s logistical capacity to deliver shots will be crucial too, said William Padula, a USC professor of pharmaceutical and health economics. Biden’s goal would be doable if the state and Blue Shield — the health care nonprofit with which California leaders have struck a controversial deal to manage vaccine logistics — create a system that can fulfill their promise to deliver several million shots each week, Padula said.

“It’s possible,” he said. “But I don’t know whether it’s probable.”

If all of that happens, eliminating eligibility restrictions on May 1 still wouldn’t mean everyone could get vaccinated right away. If it’s done wrong, Padula warned that could create a “logjam” of people seeking appointments, making it even harder for those who are less savvy to get shots even if they are at greater risk.

A better model, Padula said, would be more of a waitlist system — something California’s vaccination program doesn’t currently have. In that system, rather than furiously refreshing the MyTurn.ca.gov website every day as they hunt for open appointments, people could secure their place in line by putting their name down on May 1, and eventually get an appointment when one is available.

“They’re in the queue,” Padula said, “and they know their name will come up.”

Staff writer Marisa Kendall contributed reporting.