In Greek legend, an oracle revealed that a knot tied by King Gordius of Phrygia could only be undone by one who was destined to become the ruler of all of Asia. Alexander the Great tried to untie it but failed, after which he cut it with his sword.

The phrase now refers to any perplexing or apparently insoluble problem, and to cut the Gordian knot refers to finding a quick solution. So the attempts of Congress to reduce the U.S. budget deficit might be described as attempts to cut the Gordian knot of the budget deficit.