What term is given to the idea that the United States should give political, military, and economic support to democratic nations threatened by authoritarian powers?

The Truman Doctrine would most likely be the term you're looking for in US history. Perhaps more accurate than the phrase "authoritarian powers" would be to say that the Truman Doctrine was concerned especially about the threat of communism and totalitarianism.

The Truman Doctrine was first stated by President Harry Truman to Congress in 1947, saying: "It must be the policy of the United States to support free people who are resisting attempted subjugation by armed minorities or by outside pressures." Essentially, the Truman Doctrine pledged American effort elsewhere in the world to check the spread of communist and Soviet influence. The policy was first put into action in 1948 by providing economic support to Greece and Turkey to stave off communist movement in those countries.