What would the Foreign Policy implications of a U.S. president invoking the Monroe Doctrine today be like?

Answer 1

In a sense it never went away, it only expanded to a global level. The goal of most (if not all) nations is to increase their own relative power and influence on the international scale, if possible to the exclusion of others. The Monroe doctrine just codified this by saying that America is "the boss" of the western hemisphere, however since WW2 our government has maintained a global military presence and become "the boss" of most of western civilization.