For nearly two years, car dealers have been focused on getting more cars onto their lots amid a severe inventory crunch. Now, some are worried about how quickly they will be able to move them off.

Slim selection at dealerships since mid-2021 created a backlog of consumer demand. At many dealerships, that trend has meant most vehicles arriving from the factory are presold, often at prices well above the manufacturers’ suggested retail price.

But as new-vehicle stocks are slowly replenished, some dealers say there are signs that an uncertain economic outlook and higher interest rates are starting to dampen demand.

“There is pent-up demand from people who’ve been in the market for six or nine months and haven’t been able to find a car,” said Peter Lanzavecchia, a Marlton, N.J., dealer who sells Hyundai, Genesis, GMC and other brands. “But it’s going to dry up. We’re very concerned about 2023.”

A quarterly survey of more than 1,000 U.S. dealers, conducted Oct. 25 to Nov. 7 and released this week by Cox Automotive, shows their outlook for car sales is the gloomiest it has been since the research firm first began the poll in early 2017.

The majority of dealers who responded view the current market for selling cars as weak. Overall, they cited the economy and interest rates as the top two factors holding back their business, with a lack of inventory ranking third. Since mid-2021, limited inventory had ranked as their top concern, the surveys showed.

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“This incredible period that has produced record profits for many dealers is quickly turning into a more worrisome period,” said Jonathan Smoke, chief economist for Cox Automotive.

The findings reflect uncertain times in the car business. Signs of a possible recession typically rattle the cyclical auto industry, which normally gets hit hard in a downturn.

But despite the cloudy economic outlook, the market dynamics that have fueled strong profits for dealers and auto makers over the past two years remain largely intact: Relatively scarce vehicle supply, and a backlog of consumers who are in the market for a car and willing to pay top dollar. As a result, some auto-industry executives say the market remains healthy.

“There probably is some pent-up demand out there that is going to continue to work itself through in 2023,” General Motors Co. finance chief Paul Jacobson said last month. He expects pricing to ease some next year as economic factors deter some buyers.

Rising interest rates are one of the biggest threats to customer demand, dealers and automotive executives have said. In the Cox survey about half of the dealers who responded cited interest rates as a problem, compared with just 3% who responded that way a year earlier.

At many dealerships, a backlog of purchases meant most vehicles arriving from the factory are presold, but there are signs of softer demand.

Photo: David Zalubowski/Associated Press

Meanwhile, a falloff in the value of trade-in vehicles has started to erode new-vehicle demand, said Mr. Lanzavecchia. As used-car prices descend from record highs, new-car buyers who are trading in vehicles don’t have as much value to offset the purchase price, he said. Auto-auction firm Manheim’s index of wholesale used-vehicle prices was down 14% in November from a year earlier.

But the prices consumers are paying for new vehicles have held up better. Even while auto makers increase output, as the semiconductor shortage and other supply disruptions ease, vehicle inventories are still running thin, which has kept prices elevated.

The number of vehicles on dealership lots or en route to stores in November rose 57% from a year earlier, to 1.6 million, according to research firm Wards Intelligence. Still, that level is roughly one-third below the historical norm.

Auto executives have said they aren’t likely to boost consumer incentives—which have hovered near historic lows—until vehicle availability improves. The average new-vehicle price in November was $45,872, a record for the month, and just a few hundred dollars off the record-high set in July, according to research firm J.D. Power.

Jack Hollis, executive vice president of Toyota Motor Corp.’s

North America business, said the company’s U.S. dealers have the equivalent of about four days of vehicle supply on the ground, whereas they normally would carry more than a month’s worth. He sees constraints lasting through 2023, and expects to essentially sell as many vehicles as Toyota is able to make.

“There is still huge demand for new vehicles,” he said in an interview last week.

Car shoppers for nearly two years have expressed frustration over a lack of availability and griped about dealers charging above manufacturer’s suggested price. Some say they expanded their searches out of state to avoid paying more than the sticker price.

In November, about half of new-vehicle buyers were paying more than the sticker price, down from a 64% peak in June, according to J.D. Power.

Continued lofty prices combined with higher interest rates are keeping some buyers away, said Mike Maroone, chief executive of Maroone USA, which owns seven dealerships in Colorado and Florida.

“Affordability is a bigger and bigger issue,” he said.

The possibility of an economic downturn has caused some dealers to pay closer attention to keeping their sales staff sharp. Earl Stewart, who owns a Toyota dealership in North Palm Beach, Fla., recently expanded training sessions for his workers, pushing them to respond to customers quickly and ranking them in comparison to their peers. He even dispatched undercover shoppers, with code names like “Agent Lightning,” to test staffers.

“I’m disturbed because my salespeople have become order takers,” he said.

Write to Nora Eckert at nora.eckert@wsj.com and Mike Colias at Mike.Colias@wsj.com