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Mayor Vincent C. Gray told council members that the federal Office of Management and Budget on Monday asked for further information about his declaration that all workers were essential and had posted his plan on its website along with shutdown plans for federal agencies.

“I think we are in a good place with respect to our position,” he said.

But D.C. officials estimate the city stands to lose between $1 million and $6 million per week in uncollected income and sales tax as a result of the shutdown.

With government-run parks, monuments and museums on the Mall closed through the shutdown, the region could lose out on tourism dollars as well.

Stephen Fuller, director of George Mason University’s Center for Regional Analysis, told The Associated Press that travel and leisure spending generates about $12 billion annually for the region’s economy, or about $33 million a day in tourism business, with the main draw being the Mall.

“We’re not going to lose it all,” but business lost in leisure travel won’t be made back, Mr. Fuller told the AP. “It’s the visitors from Kansas who won’t come here or the international visitors who will now go to Chicago or stay in New York longer. It’s going to cost us something.”

Private museums, such as the Newseum, remain open and could even see a boost in visitors as tourists seek out other options after being turned away from the city’s shuttered attractions.

“We’ve been getting calls from groups who were scheduled to visit the Smithsonian museums or other monuments around the city,” Newseum spokesman Jonathan Thompson said of tour groups making contingency plans.

While Mr. Thompson said it’s too early to tell if the museum will see an uptick in visitors, he noted that the Newseum on Tuesday had double the number of walk-in visitors as it had the same day last year.