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.

Immigration has proved to be a potent political messaging tool, particularly for Republicans, who have rallied voters behind campaigns to close the border with Mexico — and denounced anything other than stringent security proposals as amnesty. And Democrats have long resisted border security initiatives without measures to grant legal status to millions of immigrants residing in the United States without permission and to expand immigration in the future.