The North Koreans break through the Pusan Perimeter. Yet MacArthur demands the war to continue. The Incheon landing takes place, as do the Home-by-Christmas offensive, and the Chinese intervention. In these cases US casualties are much higher, and Korea quickly becomes a quagmire like Vietnam.
Hoping to turn the tide, MacArthur manipulates McCarthyism and persuades Truman to send an "expeditionary force" to occupy Shanghai until China ceases its involvement.
Shanghai itself is occupied with little resistance, yet Mao continues guerrilla attacks against US troops in Shanghai, hoping the US will expand their war into China, which the US will inevitably lose. MacArthur falls right into Mao's trap, as US troops almost exactly replay the Japanese invasion of 12 years earlier. US troops commit mass atrocities when they besiege Nanking, causing widespread disgust at home. Yet the "police action" continues with MacArthur refusing to compromise until the Chinese leave Korea.
By, say, 1955, the US has lost as many troops in China and Korea as in WW2, with hundreds of thousands more troops held POWs as far away as Tibet.
Whoever is POTUS in 1956 then unceremoniously fires MacArthur, and just to be sure, finds a convenient excuse to court martial him.
In 1957, the "police action" in China ends with the US recognizing the PRC (and Korea in its sphere of influence) and promising significant financial aid, with the aim of dividing China from Moscow and taking advantage of Stalin's death.
The 50s are remembered in the US as yet another decade of war and austerity, without the noble cause of the last war. The much more sombre mood prevents the 60s from becoming as happy and free-wheeling as OTL.