OK, so I am home now and reviewing some sources. At the time that atomic release was requested, the US had approx 290 working atomic weapons (more triggers etc than that, but these are the assembled and ready to use weapons).(1)
MacArthur wanted at least 27 bombs used on various targets (or slightly under 10% of the US arsenal). The JCS were worried enough that the idea was taken seriously in late December 1950/early Jan 1951. However by mid January it was clear that the crisis had passed and the idea was shelved. (2)
So the most likely time for this to happen is during the great panic in early January. Even then Air Force General Vandenburg (the AF's member of the JCS) is likely to be reluctant to expend nukes on targets he'd consider a waste. Perhaps if the Chinese lloked like they were going to throw the UN forces out of Korea altogether then a final "screw you" may have been considered. However logistics for the Chinese makes this pretty much "Sea Lion" impossible.
There were a number of other ideas being reviewed at the time that may (or may not) have made a difference to Chinese pressure in Korea. These included a conventional bombing campaign against industrial targets in Manchuria, giving the go-ahead to the KMT to attack mainland China, and a naval blockade of the PRC.
(1) The Revolt of the Admirals
(2) Max Hasting's The Korean War