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 say 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 say. And a significant number of House Republicans have little incentive to bend because they are elected by fiercely conservative voters who detest political compromise.

It’s “a different time,” said 10-term GOP Rep. Steve Chabot of Ohio, who doesn’t always support House leaders but sympathizes with their struggles. “It’s a tougher job than it was back then to pull together a working majority.”

Chabot cited outside groups that scrutinize “every vote and everything we do” and are quick to declare “we’re not conservative enough.” With President Barack Obama seemingly more eager to veto GOP-passed bills than to compromise with Republicans, he said, “I don’t think it’s possible to do very large things until after the next election.”

Chabot’s colleagues cite other reasons why House Republican leaders — headed by Speaker John Boehner of Ohio — are suffering embarrassing setbacks despite their 245-188 seat advantage over Democrats. (Two Republican-held seats are vacant.)

GOP leaders struggle to find even a few Democratic votes when needed because moderates from both parties have largely been driven out of Congress. And congressional leaders no longer can dole out pork-barrel projects, or earmarks. For decades, their predecessors used such favors to move balky lawmakers from “nay” to “aye.”

“It’s a contentious time, with a lot of polarization,” said Republican Rep. Tom Cole of Oklahoma. “And you have fewer tools.”

“There’s no earmarks,” Cole said, and current leaders rarely turn to bare-knuckle tactics such as kicking uncooperative colleagues off plum committees. “Boehner’s style is a little bit more easygoing,” he said. “He doesn’t like to punish people.”