WASHINGTON — Conservatives in the House rebelled against their leadership on Thursday to scuttle an emergency spending measure that addressed the migrant crisis at the southern border, pushing the issue to a showdown on Friday as lawmakers prepared to leave for a five-week recess. The unexpected turmoil offered a coda to the dysfunction that has gripped the Capitol for much of the year.

The failure of the comparatively modest Republican border bill, coupled with the Senate’s own inability to even bring a Democratic alternative to a vote, emphasized how the prospects of a broad immigration overhaul — which at the beginning of the 113th Congress held great bipartisan promise — have ground to a crashing halt.

The struggle to deal with immigration, which became more urgent with the flood of tens of thousands of children at the border, succumbed to congressional infighting, driven by more conservative Republicans who balked at further government spending and President Obama’s approach on deporting the migrants.

Fissures were evident in the Republican Party, with many House members critical of their more conservative colleagues for holding up the bill, arguing that heading home for the August break having not even voted on immigration legislation would be politically damaging. The episode was also a rebuke, at least temporarily, for Speaker John A. Boehner and his new leadership team, who in an emergency closed-door meeting on Thursday told members that they were not even close to the necessary votes required to pass the bill.