This week, the National Gallery of Art turned away the prime minister of Greece, Antonis Samaras, and Adrienne Arsht, the philanthropist who underwrote the gallery’s most recent blockbuster exhibition, “Diaghilev and the Ballet Russes.” Samaras was supposed to view a Byzantine art exhibit co-sponsored by groups from his country. Arsht was set to throw a large party for patrons who wanted to visit “Diaghilev” one last time.

Both were canceled due to the government shutdown. And therein lies a lesson about why the shutdown is even worse for Washington's museum sector than you might think. In short: The Smithsonian and other federally funded museums rely in significant part on private funding — but the shutdown inhibits their ability to raise even the private funds.

While government agencies typically receive all their funds from government, Washington’s federally chartered museums are 501(c)(3) groups that operate as nonprofits. The Smithsonian museums and the National Gallery of Art receive about 70 percent of their funds from the government, which go toward maintenance and capital projects.  But the other expenses — new art, public programming, major exhibitions — are financed by private funds and donations. And these museums are already one week behind in meeting their annual goals, as the shutdown inhibits their ability to raise private funds.

While most museum workers are home and the visitors are locked out, the privately funded staff is still working. About 10 percent of Smithsonian employees are reporting to work, and some of these employees are paid through private trust accounts. That means federally funded museums are paying employees money while not open and operating.

The people who spend money in gift shops and restaurants can’t come in as long as the museums are closed. Gift shops and vendors generate millions of dollars for federally funded museums each year. Somewhere in their budgets, museums are going to have to recoup these losses.

The worst possibility, though, is that a prolonged shutdown could affect philanthropic giving. Just as Arsht couldn’t see the exhibit she underwrote, 12,000 people are being turned away from the National Gallery alone each day. 80,000 are locked out from the Smithsonian museums every day. Philanthropists may think twice before donating to museums that shut down due to congressional squabbling. One of the big selling points at the Smithsonian and the National Gallery is that these museums are funded by the federal government, and because of that, will always be free and open to visitors who otherwise couldn’t afford an entrance fee of $15 or more.

Shutdowns are a reminder that there are drawbacks to federal reliance, and that Smithsonian leadership is beholden to the whims of Congress. Prolonged closure could lead some patrons to send their gifts to the Met or MoMA, particularly if they foresee government shutdowns becoming a common feature of American politics.

If you're a big donor for art-related causes, after all, you want people to actually be able to see the fruits of your donations — not be locked out due to government dysfunction.