Even if elements of the Armed Forces sucessfully pulled off a coup, could a leftist, secular regime last for long in the Arabian Penninsula? This isn't Iraq, Syria or Egypt, where a large part of the population is secular, open to socialist ideas and cosmopolitan. I imagine tribal revolts by conservative Islamists and Royalists will spring up almost immediately (supported by Western Arms, of course, since the US, UK and France would all prefer Islamists over pro-Soviet secularists).
Could anyone imagine a left wing secularist mocking Islamists in this manner in Saudi Arabia? Even were he able to pull off a successfull coup?
What type of intervention? A CIA staged coup or an invasion? With the US already mired in Vietnam, I don't think LBJ or Nixon would want to start another unpopular war.If you have a Nasserite Saudi government, and Aramco attempts to nationalise the Saudi oil industry as in OTL, then I think you'd get American intervention.