The video drew sharp criticism from conservative groups after publication of a CNS news service article with the headline: "Smithsonian Christmas-Season Exhibit Features Ant-Covered Jesus, Naked Brothers Kissing, Genitalia, and Ellen DeGeneres Grabbing Her Breasts."
Donohue, who led the protests, said it was "doubly egregious" that the work was being featured at a museum funded partially by the public.
"Incivility is wrong. It's doubly wrong when it's funded by taxpayers," he said.
Several Republican leaders, including House Speaker John Boehner and Majority Leader Eric Cantor, said they would examine taxpayer funding for the Smithsonian in the wake of the controversial display.
"Absolutely, we should look at their funds," Georgia Rep. Jack Kingston, a member of the House Appropriations Committee, told Fox News last month. "If they've got money to squander like this -- of a crucifix being eaten by ants, of Ellen DeGeneres grabbing her breasts, men in chains, naked brothers kissing -- then I think we should look at their budget."
While the exhibition itself was privately funded, taxpayer dollars are used for general operations of the museum facilities and its staff.
The Smithsonian Institution received $636 million in federal funding in 2010. The National Portrait Gallery received $5.8 million.
In an e-mail to his staff, Smithsonian Institution president Wayne Clough suggested that he pulled the video because he didn't want controversy about the video to distract from the rest of the exhibition.
"I regret that some reports about the exhibit have created an impression that the video is intentionally sacrilegious," National Portrait Gallery director Mark Sullivan said in a statement. "In fact, the artist's intention was to depict the suffering of an AIDS victim. It was not the museum's intention to offend."
The removal of Wojnarowicz's work was unprecedented. The gallery has never before pulled a piece out of an exhibition because of public outcry, according to Smithsonian Institution spokeswoman Linda St. Thomas.
She said that prior to publication of the CNS article, the museum had received no complaints about the video, which she described as a small part of the show.
"It was a small screen in an alcove of the exhibit, and you had to push a button on the screen to activate it," St. Thomas said.
Olsoff, the New York gallery co-owner, called removal of the video "censorship."
"This is about something more than David Wojnarowicz," she said. "It's a knee jerk reaction in response to attempts by the Catholic League to draw attention to what they're doing."