For nearly a quarter century, as successive waves of migrants have tried to enter and work in the United States, presidents have appealed to Congress to address gaps in an immigration system nearly everyone agrees is broken.

Yet year after year, congressional efforts to strike a wide-ranging bipartisan deal — one that would strengthen border security measures while expanding avenues for people to immigrate to the United States in an orderly and lawful way — have fractured under the strain of political forces…