Which countries would be nearly impossible for the U.S. to conquer militarily?

Countries like Russia, China, and possibly India would be incredibly hard—or even impossible—for the U.S. to conquer due to their vast size, large populations, and challenging geography. Unless you’re Genghis Khan, taking on even one of these countries is likely beyond reach. 

If all the countries in the European Union were to unite, this combined force would probably be too strong for the U.S. to fully conquer. While the EU wouldn’t likely be able to invade America in return, it could effectively resist a U.S. invasion and force a stalemate.

In World War II, the planned invasion of Japan was seen as extremely risky. Japan had very few landing beaches, which were well-defended, and the population was expected to fiercely resist, as shown in the brutal fighting on Okinawa. Allied casualties were projected to exceed a million in a full-scale invasion.

Something like that would be politically unacceptable with the US public, which is very casualty-averse since the Vietnam War. The other country must have pulled a Pearl Harbor or 9/11 for this to even be considered. As long as North Korea doesn’t do anything silly and attack the US or South Korea/Japan directly, they are politically unassailable.