In a significant shift, Republican officials said it now seemed unlikely that the four states to vote first would all retain their cherished place on the electoral calendar, with Nevada as the most probable casualty.

Party leaders are even going so far as to consider diluting the traditional status of Iowa, New Hampshire and South Carolina as gatekeepers to the presidency. Under one proposal, those states would be paired with others that voted on the same day as a way to give more voters a meaningful role much sooner.

But in a move that would sharply limit who could participate in presidential primaries, many party activists are also pushing to close Republican contests to independent voters, arguing that open primaries in some states allowed Donald J. Trump, whose conservative convictions they deeply mistrust, to become the presumptive nominee.