WASHINGTON — Why are so many American families trapped in poverty? Of all the explanations offered by Washington’s politicians and economists, one seems particularly obvious in the low-income neighborhoods near the Capitol: because there are so many parents like Carl Harris and Charlene Hamilton.

For most of their daughters’ childhood, Mr. Harris didn’t come close to making the minimum wage. His most lucrative job, as a crack dealer, ended at the age of 24, when he left Washington to serve two decades in prison, leaving his wife to raise their two young girls while trying to hold their long-distance marriage together.