Representative Kevin McCarthy, Republican of California, is struggling to break through a wall of entrenched opposition from hard-right lawmakers even after agreeing to weaken his leadership power. 

WASHINGTON — Representative Kevin McCarthy of California, the Republican leader, toiled on Monday — the day before his party was to assume the House majority — to lock down the votes he needs to be elected speaker having so far failed to break through entrenched opposition from hard-right lawmakers.

The recalcitrance among ultraconservative lawmakers, even after Mr. McCarthy made a key concession that would weaken his power in the top post, threatened a tumultuous start to the Republican majority in the House. The standoff underscored Mr. McCarthy’s precarious position within his conference and all but guaranteed that even if he eked out a victory he would be a diminished figure beholden to an empowered right flank.

In a vote planned for around midday on Tuesday, when the new Congress convenes, Mr. McCarthy would need to win a majority of those present and voting — 218 if every member of the House were to attend and cast a vote. But despite a grueling weekslong lobbying effort, he appeared short of the near-unanimity he would need within his ranks to prevail.

A group of five Republicans has publicly vowed to vote against him, and more are quietly opposed or on the fence. Republicans are poised to control 222 seats and Democrats were all but certain to oppose him en masse, so Mr. McCarthy could afford to lose only a handful of members of his party.  

With little time left before the vote on Tuesday, Mr. McCarthy tried over the weekend to win over the hard-liners with a major concession, by agreeing to a rule that would allow a snap vote at any time to oust the speaker.

Lawmakers opposing him had listed the change as one of their top demands, and Mr. McCarthy had earlier refused to swallow it, regarding it as tantamount to signing the death warrant for his speakership in advance. But in recent days, he signaled that he would accept it if the threshold for calling such a vote were five lawmakers rather than a single member.

But that was not enough to sway the five rebels opposing him, and more dissenters emerged on Sunday night, after Mr. McCarthy announced the concession to Republicans in a conference call.