North Korea’s first congress of the ruling Worker’s Party in 36 years last week bestowed the new title of chairman on dictator Kim Jong Un, and as expected his speech stressed nuclear weapons and economic development. But behind the usual boasts and bluster, the regime of the “young marshal” is under pressure.

In late March state media began to call on North Koreans to prepare for a new “arduous march”—the regime’s term for the famine in the late 1990s that killed hundreds of thousands. An editorial in the main newspaper warned,...