With the fate of his ballroom tied up in court, President Trump is racing against the clock.

He has enlisted a team of 250 workers to push ahead with construction 20 hours a day, seven days a week to complete as much work as quickly as possible. This week, there are plans to install one million pounds of rebar and pour 3,000 cubic yards of concrete for a project that is now two-thirds complete, the administration said in a court filing.

Now, with the matter pending before the Supreme Court, the Trump administration is making a practical appeal to the justices: The ballroom is simply too far along to be stopped now.

“His strategy clearly is to change the reality on the ground so that instead of preserving the status quo, those who rightly invoke the law against what he’s doing are put in a position of having to undo something that is already a fait accompli,” said Laurence H. Tribe, an emeritus university professor of constitutional law at Harvard.

For years, Mr. Trump has argued that the White House should have its own ballroom, saying it was a matter of prestige on the world stage. A ballroom, he said, would allow officials to hold big events for special guests without needing to erect a tent on the South Lawn.

In recent months, as preservationists and other critics have tried to halt or at least slow down the project, Mr. Trump has offered a new justification: national security. Essentially, Mr. Trump is treating the ballroom and the military bunker underneath it as one and the same.

The bunker — officially known as the Presidential Emergency Operations Center, or PEOC — was built during World War II beneath what was once the East Wing, which Mr. Trump tore down last year to make way for his ballroom.

Now, he speaks about the two projects in the same breath.

After an armed man rushed the White House Correspondents’ Association dinner in April, for example, Mr. Trump said on social media that the mayhem had proved the need for “the Militarily Top Secret Ballroom currently under construction at the White House.”

Mr. Trump demolished the East Wing last October without seeking any approvals or submitting construction or demolition plans to Congress. While he did bring the project before two review panels whose leaders he had appointed, Mr. Trump has continued to change the plans from the designs they authorized.

Several federal court rulings have found that the president exceeded his authority by moving ahead without congressional approval, but the decisions have been paused pending appeals — which means the construction can go on at least until Friday, when an appeals court order to halt the aboveground construction goes into effect.

The case is also pending before the Supreme Court.

Last week, the Trump administration told the Supreme Court the president was adding flashy golden seals on the outside of the ballroom, a design element that was never submitted to the Commission of Fine Arts.

Joshua Fisher, the director of White House management and administration, told the court that a concrete-and-steel superstructure had already been built that stretches five stories deep and 70 feet high.

Mr. Fisher said 80 percent of the rebar for the project had been placed, and the concrete poured.

He said $335 million of the $400 million needed for the project had been raised from private donors. He estimated the construction was 65 percent complete.

Mr. Fisher said that the ballroom’s columns were being carved by renowned Italian artists, and that the building would be sturdy enough to withstand a nuclear blast.

“Given the current progress, the superstructure is beyond the point of return,” Mr. Fisher wrote. He added that even if the Supreme Court ordered the plans for the building altered or the building taken down, “there would be no way to do so.”

The message was clear: The ballroom cannot be undone.

But in a filing on Tuesday, the preservationists challenging the project told the justices that the administration was trying to “outrun judicial review” by suggesting that it was too late to stop the construction.

“They tell this court that because the ballroom is being built with the type of concrete used ‘in nuclear power plants,’ it will soon be ‘virtually impossible to deconstruct,’” according to the filing.

Lawyers for the National Trust for Historic Preservation in the United States, a nonprofit chartered by Congress to guard America’s historic buildings, said the administration had intentionally accelerated construction “in an effort to put their illegal ballroom” beyond judicial intervention.

They have pointed to the Constitution and several federal laws that state Congress must approve such a project. One federal law says, “A building or structure shall not be erected on any reservation, park or public grounds of the federal government in the District of Columbia without express authority of Congress.”

Lower court judges have sided with the preservationists, ruling that Congress must first sign off on the expansion and renovation of the White House complex.

“Efforts to foil judicial review and arrogate Congress’s exclusive powers should not be rewarded with a stay that allows petitioners to complete a ballroom they lacked any authority to commence in the first place,” said the trust’s lawyers, led by Thaddeus A. Heuer.

In its filing on Tuesday, the trust suggested that the Supreme Court temporarily halt the aboveground work and then quickly schedule oral arguments for October or November to formally decide whether the project can proceed. If the justices do not press pause now, the trust said, the project is on track to be substantially finished this fall and it will be too late.

D. John Sauer, the solicitor general, has argued that the ballroom is inextricably linked to the broader national security needs of the White House complex. He said the structure is built with hardened concrete, steel and rebar; protective missile-resistant columns, roofs and beams; droneproof ceilings and roofs; and bullet-, ballistic- and blastproof glass. It includes bomb shelters, state-of-the-art hospital and medical facilities, protective partitioning between all areas of the building, top secret military structures and equipment, military-grade venting, a single integrated air conditioning and heating system, sniper nests and a drone port on top.

Mr. Sauer has also pushed back on the assertion in the unfavorable appeals court ruling that Mr. Trump is a temporary tenant, not the owner, of the White House. “The president of the United States of America is not a tenant, but rather the sole, elected head of the executive branch,” he wrote, adding that other presidents had taken steps to renovate the White House.

The Supreme Court’s conservative majority has often been receptive to the Trump administration’s efforts to expand presidential power, but it has also ruled against some of Mr. Trump’s signature initiatives. The justices are expected to issue an order before the appeals court ruling that would halt construction takes effect on Friday.

Kimberly Wehle, a law professor at the University of Baltimore, said that Mr. Trump had been pushing to expand the powers of the presidency for years, and that attempting to construct a massive new building on White House grounds without lawmakers’ approval is his latest step.

“It’s so symbolic that he literally bulldozes the White House and says, ‘What are you going to do about it?’” she said. “They’re making this general generic argument that ‘I’m the president, so it’s national security, I can do whatever I want.’ That is a very steep, slippery slope into unlimited power in the presidency.”