By Madeline Holcombe, CNN

(CNN) -- The US recorded its second-highest one-day tally of Covid-19 deaths Tuesday, and experts say rising coronavirus hospitalizations could portend higher daily counts in the coming weeks.

There were 2,597 new deaths reported across the US, bringing the country's overall Covid-19 death toll to over 270,600, according to data from Johns Hopkins University. The only day to top that daily total was April 15, when six more deaths were recorded.

The country's daily average of Covid-19 deaths across a week is 1,531 -- above its summer high of around 1,130 but lower than the US pandemic peak above 2,240 in late April.

But as coronavirus hospitalizations rise, the number of daily deaths is predicted to get worse, with various experts recently warning that it could regularly surpass 2,000 and 3,000, and perhaps approach 4,000.

Recorded hospitalizations already are at unprecedented levels. More than 98,600 Covid-19 patients were in US hospitals Tuesday -- the most counted during the pandemic, according to the COVID Tracking Project.

Health experts say they expect cases and hospitalizations to swell further in the coming weeks, when infections from Thanksgiving gatherings start to manifest.

The world appears to be moving closer to available Covid-19 vaccines: The United Kingdom on Wednesday became the first Western nation to approve one, and the first doses are expected to be be rolled out across that country starting next week.

And two companies are preparing to ship out vaccines in the United States, anticipating the US Food and Drug Administration will give them emergency approval this month.

But initial supplies in both countries will be limited, and the wider population won't have access to them until months into 2021.

States push back against climbing records

Tuesday was a record-breaking day for coronavirus devastation in many states, and local leaders are pushing back with new measures to combat the virus.

Oregon reported its highest number of deaths reported in a day. Texas set its record for coronavirus cases reported in one day, at more than 15,000. And Mississippi has more Covid-19 patients in hospitals than ever before, at more than 1,000, state officials said.

Mississippi since late October has had a mask mandate in certain counties where the spread of the virus was worst. On Tuesday, the governor added 13 counties to that list -- meaning the mandate is now in 65% of the state's counties.

"This is a time when the virus is extremely present," Gov. Tate Reeves told reporters. "The risk is higher of catching it because of the number of cases that we're reporting, there is more virus in the communities."

Kentucky Gov. Andy Beshear called Tuesday the state's "worst day ever" for the coronavirus by "virtually every measure."

"It is the deadliest day that we have had," Beshear said. "If we don't all do our part, if we try to be the exception, then slowing down this thing won't work, and we will lose a lot more Kentuckians we love and care about."

California's Los Angeles County also had its "worst day" yet when it came to cases and hospitalizations, according to county Health Director Dr. Barbara Ferrer.

"However, it will likely not remain the worst day of the pandemic in Los Angeles County. That will be tomorrow, and the next day and the next as cases, hospitalizations and deaths increase," she said.

A modified stay-at-home order went into effect in the county Monday, prohibiting outdoor dining and gathering with people outside a single household.

Nursing home cases reach highest peak since spring

Nursing homes, which were hit hard early in the pandemic, reported their highest week of new coronavirus cases since the spring, the American Health Care Association and National Center for Assisted Living (AHCA/NCAL) said in a report published Tuesday.

"Our worst fears have come true as Covid runs rampant among the general population, and long-term care facilities are powerless to fully prevent it from entering due to its asymptomatic and pre-symptomatic spread," said Mark Parkinson, president and CEO of AHCA/NCAL, in a statement.

Between mid-September and the week of November 15, there was a 177% rise in new weekly nursing home cases nationwide. The rise in cases has been accompanied by a rise in coronavirus deaths in nursing homes.

Nursing homes in the Midwest were particularly hard hit, with a more than 400% increase in weekly cases since mid-September.

The increase is correlated with the nationwide surge in cases, and health experts say increased spread in the community is a good indicator that cases will surge in nursing homes.

"Given the fact that our elderly population is the most vulnerable and the rising level of Covid across the US shows no signs of stopping, it is paramount that the Centers for Disease Control and Prevention (CDC) provide the highest priority for the vaccine distribution to long-term care residents and staff," Parkinson said.

Health care workers and long-term care patients will be vaccinated first

A widespread distribution of vaccines may still be months away, but the US is preparing to ship out the first wave of inoculations -- and health care workers and long-term care patients are at the top of the list to receive them.

Federal officials expect to have 40 million doses of the coronavirus vaccine available by the end of December, but those doses will not all be available at once, CDC vaccine advisers were told Tuesday.

The CDC's Dr. Sara Oliver told the Advisory Committee on Immunization Practices that the agency expects between 5 million and 10 million doses to become available each week for the first few months as vaccine makers ramp up manufacturing.

The panel recommended Tuesday that heath care and long-term care workers get inoculated first as vaccines are rolled out.

Vaccine candidates from Pfizer and Moderna are awaiting emergency use authorizations in the US, with an FDA panel expected to meet about whether to authorize them on December 10 and December 17, respectively.

Assuming the vaccines are authorized, the vaccines' first shipments could happen December 15 and 22, respectively, according to a document from the federal government's Operation Warp Speed.