Wikipedia:

The Washington Monument syndrome, also known as the Mount Rushmore Syndrome, or the firemen first principle, is a political tactic used in the United States by government agencies when faced with budget cuts. The tactic entails cutting the most visible or appreciated service provided by the government, from popular services such as national parks and libraries to valued public employees such as teachers and firefighters. This is done to gain support for tax increases that the public would otherwise be against. The name derives from the National Park Service’s alleged habit of saying that any cuts would lead to an immediate closure of the wildly popular Washington Monument. Critics compare the tactic to hostage taking or blackmail.

Although the strategy usually intends to highlight the government’s value to voters, it can also be aimed at lawmakers themselves. Faced with budget cuts in the 1970s, Amtrak announced plans to cease train routes in the home districts of several members of Congress.

The term was first used after George Hartzog, the seventh director of the National Park Service, closed popular national parks such as the Washington Monument and Grand Canyon National Park for two days a week in 1969. In response to complaints, Congress fired Hartzog and restored the funding.

Hat tip to Walter Olson.