As a result, the campaigns are preparing for a marathon delegate battle, and have begun building organizations in territories as far-flung as Guam and American Samoa. An adviser to Mr. Cruz’s campaign, Dennis Lennox, has island-hopped through the Pacific this month, discussing local issues like the airfares between Honolulu and Pago Pago, in search of a stray delegate who might support the senator. And on a conference call with donors the morning after Wednesday’s debate, Danny Diaz, the manager for Mr. Bush’s campaign, ran down its operations in states well beyond New Hampshire and Iowa, according to a participant on the call.

The prospect of a long and contentious nomination fight is only one reason for concern. The three-hour debate, at the Ronald Reagan Presidential Library near here, suggested that Republican leaders had yet to realize their hope of keeping primary contenders from moving far to the right, complicating a general election bid, as happened to Mitt Romney in 2012. The candidates staked out conservative positions on a variety of topics — immigration, abortion, same-sex marriage and vaccinations for children — that, if appealing in such early Republican states as Iowa and South Carolina, could prove problematic in a general election.

In the starkest sign of how unsettled the situation is, what once seemed unthinkable — that Mr. Trump could win the Republican nomination — is being treated by many within the Republican establishment as a serious possibility. And one reason his candidacy seems strong is a change by the party in hopes of ending the process earlier: making it possible for states to hold contests in which the winner receives all the delegates, rather than a share based on the vote, starting March 15, two weeks earlier than in the last cycle. Ten states have said they will do so.

If Mr. Trump draws one-third of the Republican primary vote, as recent polls suggest he will, that could be enough to win in a crowded field. After March 15, he could begin amassing all the delegates in a given state even if he carried it with only a third of the vote. And the later it gets, the harder it becomes for a lead in delegates to be overcome, with fewer state contests remaining in which trailing candidates can attempt comebacks.

“Somebody like Trump, who is operating in a crowded field, could put this contest away early if the crowd doesn’t thin out,” said Eric Fehrnstrom, who was a senior adviser to Mr. Romney.

Steve Schmidt, a senior adviser to Senator John McCain of Arizona when he ran for president in 2008, said Mr. Trump could also be helped by the fact that candidates like Ben Carson and Carly Fiorina, with thinner financial resources and therefore likelier to run out of money, are, like Mr. Trump, political outsiders. So their supporters would be more inclined to fall in behind Mr. Trump than, say, Mr. Bush or Senator Marco Rubio of Florida.

“There is a bubble of delusion among Republicans and Democrats in Washington, D.C., with regard to their parties’ respective nominating processes,” Mr. Schmidt said. “There is no magic date upon which the air will come out of the Donald Trump balloon. The notion that Donald Trump cannot be the Republican nominee is completely and totally wrong.”