WASHINGTON — Whether the issue is immigration or federal budgets, Republicans keep learning a bitter lesson: Their sizable and near-historic congressional majority doesn’t necessarily mean they can govern.

House Republican leaders confronted that truth again this week when fiscal conservatives unexpectedly blocked a leadership plan for the new federal budget.

The struggle, which pits Republicans who want a more robust military against those bent on cutting spending, will have to be resolved later in the full House.

Even if that happens, however, lawmakers said GOP leaders will still confront deep ideological divisions that could wreak chaos later this year when it’s time to raise the debt ceiling, fund the government and address other big issues that fire up conservative talk shows.

GOP leaders lack some of the disciplinary tools their predecessors had, colleagues said. And a significant number of House Republicans have little incentive to bend because they are elected by fiercely conservative voters who detest political compromise.