In addition, the history of space projects, big and small, is that they are almost never completed on time.

These factors seem to make it unlikely that astronauts will set foot on the moon during a second term of Mr. Trump’s presidency, if he is re-elected. Still, pursuing this goal could help speed the status quo at NASA. That might make it more likely the agency could make the original 2028 timetable, or even move it up a year or two.

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Vice President Mike Pence has been leading the administration’s space policy. As chairman of the National Space Council, which coordinates off-planet issues among federal agencies, he has spoken of the moon mission in sweeping and urgent language.

“Failure to achieve our goal to return an American astronaut to the moon in the next five years is not an option,” he said in March when announcing the 2024 deadline

This was a swerve for NASA.

In mid-March, the Trump administration’s budget request to Congress still followed a timeline for reaching the moon in 2028.

But a week later, Mr. Pence told Mr. Bridenstine that the White House wanted to accelerate the moon landing to 2024, setting off a rush of revisions, Mr. Bridenstine said.

NASA officials have not disclosed the total budget for a 2024 moon landing, only that they expect the cost to rise for at least the next couple years.