Polls now show that Mr. Trump has a clear advantage in Indiana, where 57 delegates are at stake. A survey conducted by Marist College for NBC News and The Wall Street Journal found Mr. Trump leading Mr. Cruz by 15 points there, and close to capturing an outright majority of the vote. Gov. John Kasich of Ohio was in a distant third place.

Mr. Cruz has signaled that he intends to forge ahead irrespective of the outcome in Indiana in a bid to block Mr. Trump from winning the 1,237 delegates required to claim the nomination. He spent part of the weekend campaigning in California, which is among the last states to vote, on June 7, and collected the endorsement of former Gov. Pete Wilson, who warned that Mr. Trump would doom the party as its nominee.

But Mr. Wilson conceded in an interview on Monday that a defeat in Indiana would imperil Mr. Cruz’s path forward. To win California, Mr. Wilson said, “the first thing he needs to do is win in Indiana.”

Without such a victory, Mr. Wilson said, “I think it’s much more difficult. The nearer that Trump gets to having the magic number, the more difficult it is.”

Republican strategists opposed to Mr. Trump acknowledge that losing Indiana could break the back of the organized resistance to his candidacy and relegate Mr. Cruz to the role of a symbolic dissenter on the right. Mr. Trump has said that a victory in Indiana on Tuesday would effectively resolve the race in his favor.