What qualifies as a Second Civil War?
Must it be entire states trying to seceed, rather than a class/race war?
Does it have to include the South once again in rebellion, since the Civil War was very much South vs. US?
Must it be on the same scale as the Civil War?
At a reasonable most, I think you could get race riots that create a formation of militias that the federal government, for one reason or another, has trouble confronting.
Otherwise, I'd say that it's near ASB to have a serious second Civil War in the US with a POD post-WW2. By then the South was mostly reconciled to the Union, and no other region has ever had a serious alternative culture. With trains and planes and cars, anyone and everyone in the US lives in every state. No longer is it normal for a family to have lived on the same land for generations; not having a single populace seriously harms sectionalism.
Plus, radio and the movies have created a blending of American culture. Cultural differances disappear when everyone's been listening to the same songs and the same commercials and watched the same actors for generations. Regional accents lessen, values become more standardized, differances for conflict are ironed over.
Even direct foreign intervention is hardly possible against a nuclear superpower. Even in the military's dark days post-Vietnam, WW3 wouldn't have been anything close to acceptable for the Soviets.
However, there are interesting ideas you could use to start an interesting situation.
The government could be lost in a decapitation strike, and a military junta/dictatorship takes over. A farce of democracy is continued, but after the Cold War is won a popular revolt (with blood shed in battles between troops loyal to the govt. and those who joined the people) takes over the nation, which is resisted for awhile by the military.
Or (to take a contingency plan I love), the Reds win in the Italian Civil War/elections, and per a contingency plan Sicily is annexed by the US and rushed into statehood to keep control of the Mediterranean ,with the Mafia's assistance on the ground. However, the Reds in Italy infiltrate and start an insurgency that tries to take Sicily out of the Union, a de facto Civil War in a far away state.