Union officials, who had denounced the plan to close the Capitol overnight as an effort to silence critics, called the reversal a capitulation by Mr. Walker’s administration.

“Cooler heads prevailed,” said Jim Palmer, the executive director of the 11,000-member Wisconsin Professional Police Association. “They had said they were going to clear the place out, and then they thought the better of it. Now it’s clear that law enforcement professionals are running the show.”