Early rift over immigration exposes House GOP’s tough path to consensus

House Republicans’ attempt to bring a border security bill to the floor as early as this week was thwarted after backlash from more moderate Republicans, delaying not only a pledge Speaker Kevin McCarthy (R-Calif.) made to a handful of lawmakers but also the fulfillment of a key campaign promise to a Republican base eager for tougher immigration laws.

The bill, introduced by Rep. Chip Roy (R-Tex.) and co-sponsored by 58 Republicans, would empower the Homeland Security secretary — currently Alejandro Mayorkas — to unilaterally bar all undocumented migrants from entering the United States through...