South American countries have an army. Bribing them/threatening them into attacking the US would cause them to redirect there forces into attacking South America. This would leave European forces struggling. The Russians got supplies from the states because the Germans blew up alot of Soviet factories. Germany would retake loss ground. France would end up open to attack and that would result in leaving the UK open for an attack by German forces as the V2 rockets would be back in range.
"Hey South America, we're totally getting out asses handed to us. Could you please attack America? Not convinced? Take all this Jewish gold? Not enough? Alright, i have one billion men in reserve to attack you if you dont!"
You fail to realize how much of a third world continent South America is. Even if they attacked America they wouldn't stand a chance.