" Big Stick ": Here, from a speech in Chicago on April 2, 1903 on the Monroe Doctrine, is the full "big stick" quote by Theodore Roosevelt:
Boasting and blustering are as objectionable among nations as among individuals, and the public men of a great nation owe it to their sense of national self-respect to speak courteously of foreign powers, just as a brave and self-respecting man treats all around him courteously.
But though to boast is bad, and causelessly to insult another, worse, yet worse than all is it to be guilty of boasting, even without insult, and when called to the proof to be unable to make such boasting good. There is a homely old adge which runs: "Speak softly and carry a big stick; you will go far." If the American Nation will speak softly, and yet build, and keep at a pitch of the highest training, a thoroughly efficient navy, the Monroe Doctrine will go far.
" Monroe Doctrine ": Here's the link to a US Government resource on the Monroe Doctrine.