I will put my ideas together. So. like I said before, Kennedy doesn´t die, get reelected, keeps the US out of Vietnam. 1968 is a democratic year, president becomes Bobby Kennedy or Humpfrey (basicly our "Lyman".). 1969 S.Vietnam collapse and its starts a discussion about what went wrong with the US foreign politic. The official answer of the goverment is, "we depend to much on right-wing puppet regimes". The Shah is seen as such a puppet and some wise guys in the state department have the idea to replace him with a "progressive" republican regime. There are some talks with persians officers and a coup is staged. Things go very wrong, the Shah and his family is slaughtered and the new maximo leader in Iran is a rather leftwing-nationalist, who nationalize the complete oil-industry, calls Israel a colonialist regime and makes a demonstrative visit in Moscow.
There is panic in Washington and the CIA organize a counter-coup, with support of the shia cleric (and a special Ayatollah). The coup is just half successful. It fails in Teheran, but a Islamic Government is established in Quom, which have control of South Iran (and most of the oil) and in the next month it looks like the government in Teheran will collapse. This is the moment the Soviets intervene. Official they just help the still legitimate Iranian government. At the beginning the Islamic forces are no match for the Soviets (Islamic guerilla will soon start to be a great problem for the Soviets, but this still lays in the future)
The USA send forces to Iran, but things doesn´t look good. Big US-fighters, more useful for carrying a nuke then for air fights, gets shot down by small soviet fighters, Mig 25 slaughters B 52 bombers, airmobile US-unit gets overrun by soviet tanks. The Generals (especially the General who commands the US air units in Iran, lets call him Scott) call for a nuclear demonstration, but the president says no. He decides in his mind, that nothing, even an american defeat is worth a nuclear war. Then short for Quom, the Soviets stops. There logistic situation is a nightmare, unrest in the occupied territories grows and they don´t want to push the Americans to far.
All this happened 1972, shortly before the presidential election. The president still gets reelected because:
a) He was very popular before the election
b) There is still a rally-around-the-flag situation
c) At the moment the public doesn´t know what a big clusterfuck the whole things was and still thinks heroic US-troops stopped the evil Russians
d) The pro-democratic media praise the president for preventing a nuclear war
But things goes downhill fast after the election. The Iran-war had let to an oilprice-shock , which throws the USA in a recession. The president makes an agreement with the Soviets, which accept de facto the Division of Iran. The Islamists (especially a certain Ayatollah) are furious and throw the US troops out. The president doesn´t care. He looked into a nuclear abyss and don´t want this to happen ever again. He is realistic enough to see, that complete nuclear disarming is impossible, but he signs a treaty with the Soviets (negations for such a treaty were running since the 1960th) which should lead to a massive reduction of US strategic (and tactical) nuclear weapons. The president push the treaty through the Senat, before his approval ratings go in free fall. He talks about a no-first-use-doctrin and it seems he will abound NATO-strategy. Some start to believe, that the president had a nervous breakdown during the Iran war and is starting to lose his mind. Some cabinet-members start to read the 25. Amendment really carefully. The background about the Iran-mess leaks out and bring also back some focus about what happened in Vietnam. The approval ratings of the president fall on a level which made Nixon 1974 IOTL look good.
The president ignores all his critics. He is on a mission to save the world from a nuclear holocaust. His only gesture to the Hawks is, that he makes Iran-war hero General “Scott” Chief of Staff, not knowing that “Scott” is deeply traumatized by what he saw as treason of the president at the soldiers fighting in Iran. Things starts to get interesting.