Fred Halliday is a little harsh here, but there is some truth to this:
‘Hearts and Minds: Term used in counter-insurgency operations of 1950’s and 1960’s, by the British in Malaya and the Americans in Vietnam, to denote attempts to win over the often brutalised and terrified local population. Euphemism for propaganda, bribery and intimidation.
Notably absent in response to 11 September and the run-up to the March 2003 invasion of Iraq, where emphasis was on use of military power (cf. Shock and Awe), but then reappeared in the face of widespread Iraqi opposition to the US presence in 2003-4. This is reflected in statement, of some historical condescension, by then-National Security Advisor…Condoleezza Rice: ‘The hearts and minds issue is back.’