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Robert Farley in "The National interest" concludes that it would have been a very bad idea indeed.
"Nuclear escalation on the Korean Peninsula would have gone terribly for everyone involved. The United States would have caused dreadful pain to uncertain strategic advantage, potentially pushing the Communist powers to escalate. The physical and human terrain of Korea would have endured awful suffering. And perhaps most importantly, the world would have lost the nascent nuclear taboo, a sense among policymakers that atomic weapons differed in some meaningful sense from other kinds of explosives, and that their practical use portended something momentous."
On that last point (the undermining of the nuclear taboo) where would we see that go in effect? Tactical nukes to relieve the French at Dien Bien Phu look like the next step. And after that?...