United Airlines Holdings Inc.,

for instance, said it expects to carry an average of 420,000 passengers a day from Dec. 16 through Jan. 3, about 5% more than the daily volumes over Thanksgiving.

Delta Air Lines Inc.

said the 7.8 million customers it anticipates between Dec. 17 and Jan. 3 would be the most since before the pandemic began in 2019, and more than double the number who flew Delta during the holidays in 2020.

Air travel has been subject to wild swings since the start of the pandemic, which have made it challenging for carriers to predict demand. A surge of Covid-19 cases and the rapid spread of the Omicron variant around the world have prompted abrupt slowdowns over the course of just a few days for some restaurants and shops—a phenomenon that could still affect travel as people make last-minute decisions about whether to call off plans.

For now, several U.S. carriers say they still expect bustling flight activity even as countries around the world clamp down on travel, restaurants curtail hours and offices send workers home again to counter the rising case numbers.

U.S. airports are already filling up, with more than two million people passing through daily for five straight days through Monday, according to the Transportation Security Administration, the longest stretch above that threshold since the week of Thanksgiving. Monday’s passenger volumes of 2.1 million were down about 16% from 2019 levels.

Those who are still planning to travel or spend time with loved ones in the coming weeks find themselves facing difficult choices, however.

Brad Wilson, 37 years old, canceled a planned trip to New York last weekend, in part to make sure that he can safely keep his plans to visit family in Michigan for Christmas. When he originally booked the New York trip back in October, the situation seemed stable, but his confidence started to wobble last week when he began hearing about long lines for testing there. A number of Broadway shows canceled performances, throwing his plans for the weekend into question. Then two friends in the city tested positive for Covid-19, despite having been vaccinated and having had booster shots.

“I’m going to basically lock down until I fly out on the 23rd,” he said Friday.

Airline executives have said the ups and downs of pandemic travel demand have gradually become less jarring over the past year and a half. New waves of cases and variants still affect bookings, but they said declines have become less pronounced. Delta and

Southwest Airlines Co.

both raised revenue guidance for fourth-quarter earnings in recent weeks, citing higher demand and ticket prices.

Delta said last week that it is closely monitoring changes in customer behavior and government responses to the Omicron variant, saying there has so far been “limited impact,” with bookings slowing in international markets that are subject to increased travel restrictions.

Delta Chief Executive

Ed Bastian

on Tuesday raised the prospect that the Omicron surge could affect the airline’s staffing levels. Mr. Bastian, along with the airline’s chief health officer and a medical adviser from Emory University School of Medicine, wrote to the Centers for Disease Control and Prevention on Tuesday, asking that it reconsider its guidance for 10 days of isolation following infection for fully vaccinated individuals.

“With the rapid spread of the Omicron variant, the 10-day isolation for those who are fully vaccinated may significantly impact our workforce and operations,” they wrote, adding that it could exacerbate worker shortages and create disruptions. The executives suggested a five-day period of isolation and testing protocol.

The CDC didn’t immediately respond to a request for comment.

U.S. domestic bookings have slipped some, falling about 16% the week of Dec. 6 from the previous week, though they remained at 65% of 2019 levels, according to the most recent available data from travel analytics firm ForwardKeys. Domestic U.S. demand has been much more stable than appetite for flights to Europe and flights within Europe, said Olivier Ponti, vice president of insight at ForwardKeys.

“The latest outbreak has had a noticeable impact on air travel, but not all markets have been equally affected,” he said, adding that the collapse in European travel “appears to have stabilized” in the first week of December.

A spokeswoman for

American Airlines Group Inc.

said domestic demand remains strong, but new testing and quarantine rules have had a damping effect on some international travel.

One sign that travel is still strong: Mitzi Kramer of Nebraska said she wanted to go to Disney World—and still would—but couldn’t get theme-park reservations, and hotel rooms she was interested in on the property were running about $900 a night.

“I tried,” she said. “I’ll just pass this year and maybe go this spring.”

A Disney spokesman said there are a range of hotel prices, including less expensive options.

Airlines Reporting Corp., which tracks tickets sold by U.S. travel agencies, said sales levels were slightly better in the week ended Dec. 19 than the previous week. “So far, we’re not seeing a profound impact on bookings due to the new variant,” said Chuck Thackston, managing director of data science and research at ARC.

As a result, carriers have stuck to their planned schedules for the holiday season, anticipating that most people won’t abandon their plans.

A bigger test, according to John Grant, chief analyst at airline-data firm OAG, will come in January, when companies will decide whether to allow their employees to resume traveling or to keep them grounded while the Omicron variant is still raging. Airlines might respond by cutting first-quarter flying, or they may anticipate that the variant will pass quickly, Mr. Grant said.

Juliana Olarte is still on the fence about a New Year’s trip to an all-inclusive resort in Cancún, watching to see how case counts in the area hold up. It is hard to know what to do, she says. Staying in New York, where she lives, might not be much safer as Covid-19 cases surge there, but she doesn’t want to unwittingly contribute to the spread of the disease.

Just in case, Ms. Olarte said she decided to propose to her girlfriend in New York on Monday, rather than in Mexico. “I’m just too stressed about the trip potentially getting canceled,” she said.

She added: “We waited basically two whole years to make the call and say we’re ready to travel internationally. Of course, the second we’re about to leave, there’s a surge.”

Corrections & Amplifications
A Disney spokesman said there is a range of hotel prices at the resort. An earlier version of this article incorrectly said it was a spokeswoman. (Corrected on Dec. 21)

Write to Alison Sider at alison.sider@wsj.com