The $1.6 billion quest to build America’s tallest skyscraper in…Oklahoma

Instead of capping the buildings at the Boardwalk at Bricktown at 345 feet, he’s now thinking one should top out at 1,907—more than twice the height of the tallest building in town, and the biggest in the U.S.

“We figure it would be iconic," said Matteson, a California-based developer who briefly made tabloid news by dating one of the Real Housewives of Beverly Hills.

Many offer other names for Matteson’s planned Legends Tower: The Redneck Burj Khalifa, The Burj Khaloma, The Jetsons Meets Las Vegas and Hot Pie in the Sky.

Oklahomans tend to admire Matteson’s bold vision, but many question whether the supertall building, higher than New York’s 1,776-foot One World Trade Center, would ever be built in a stretch of America better known as the place “where the wind comes sweepin’ down the plain."

Matteson insists the mostly residential, 134-story tower can work given the city’s strong growth and says the project is fully financed, though he declined to provide details on his backers.

And then there is the weather.

“I’ll ask you the question that many people ask me every time this project comes up: ‘How are you intending to build a tower this tall in the wind and storms and tornadoes we have in Oklahoma City?’" asked Planning Commission Chairman Camal Pennington.

Rob Budetti, managing partner of AO, the project’s California-based architect, said engineers plan a core of concrete walls between 4- and 6-feet thick surrounding the elevator shaft, and windows that can stand the force of a tornado without shattering or being sucked away. “It is probably one of the safer places to be," he said.

“I don’t know if you’re going to catch me at the top," quipped Pennington.

Meeting at City Hall, commissioners had already approved zoning for a carwash for tractor tailors by the time they reached the skyscraper project, glamorously dubbed as a SPUD, or Simplified Planned Unit Development.

‘A bit tacky’

After hashing it out for about an hour, they ultimately recommended the city council approve removing the height restrictions for the $1.6 billion four-building project, which also includes a lagoon and boardwalk amid restaurants and entertainment. (Pennington says he hopes the building happens, despite his fear of heights.)

But they put off a decision on large LED-style signs that would be draped above street level on the lower floors of the buildings and other lighting that would crawl up the sides of the tower.

“The flashing lights are a bit tacky for Oklahoma City," complained Cynthia Ciancarelli, a local resident who spoke against the project. “We’re not Vegas, we’re not Times Square."

After long riding the booms and busts of the oil-and-gas industry, Oklahoma City has been thriving and diversifying in recent years.

Leaders in the city of 700,000 pride themselves on using a 1-cent sales tax to fund projects such as a tree-lined canal with tour boats that ferry visitors through the Bricktown entertainment district, sleek streetcars, a minor-league ballpark and a new convention center. These attractions, along with plans for a new arena for the Thunder pro-basketball team and a pro-soccer stadium, bode well for the project, Matteson said.

Still, his ambitious plans fall short for some.

“LMAOOOOO," tweeted Hayden Clarkin, a New York-based transportation consultant who goes by the Transit Guy on social media, after seeing how the building would tower over the vast expanse of the city, with a few much smaller buildings peeking up from downtown.

“If you talk to 1,000 Americans and say, ‘Where do you think the tallest building in America should be?’ I don’t think anyone would pick Oklahoma City," he said.

Economist Jason Barr, whose book “Cities in the Sky" comes out next month, said the proposed tower stretches beyond what he calls the economic height of a building—the height that makes economic sense—and goes well into ego height.

“It would pencil out in New York, it would pencil out in Chicago," he said, “but statistically I can’t see it penciling out in Oklahoma City."

Barr also wonders about the rationale for an observation deck. “I’ve never been to Oklahoma City, but what do you see when you go to the observatory? Prairie or whatever? I can’t imagine that’s something that would draw a lot of people," he said.

Internet memes have placed a U-Haul truck atop the tower, like the one currently atop the 6-story U-Haul facility next door.

Aubrey Wilkinson, manager of U-Haul Moving and Storage of Bricktown, isn’t a fan of her proposed neighbor. “Nobody knows if it’s going to survive Oklahoma weather, and if that’s the case, I’m probably the first one to go," she said.

When Mike Allen, staff cartoonist for a local online publication NonDoc, learned the building’s height was chosen to honor Oklahoma’s 1907 founding, he had a question: Why stop there?

His cartoon envisions the developer going for 2,800 feet, the number of calories in Oklahoma’s official state meal, which consists of BBQ pork, sausage with biscuits and gravy, chicken-fried steak, fried okra, squash, black-eyed peas, grits, corn, cornbread, pecan pie and strawberries.

“When they first showed the renderings, I just burst out laughing because it just looks so absurd compared to everything else around here," Allen said.

Jamie Vesay and Suzanne Johnson, a couple visiting from Omaha, walked along the Bricktown Canal on a recent day.

“It is the future. See who can build the biggest one," said Vesay, a 61-year-old film-location scout and producer.

Johnson, also 61, who works in the convention business, was less enthusiastic. “The city still has kind of a nice Midwest feel to it, and a supertall building would just be obnoxious. And are we into obnoxious?"

Write to Joe Barrett at Joseph.Barrett@wsj.com