He was beating Mr. Trump in the obscure, internecine delegate fights that could end up deciding the Republican nomination for president.

"This is how elections are won in America," Mr. Cruz gloated after walking away with the most delegates in Wyoming last month.

Now, as he faces a potentially candidacy-threatening contest on Tuesday in Indiana — where a new NBC News/Wall Street Journal/Marist poll, released Sunday morning, showed him trailing Mr. Trump by 15 percentage points — Mr. Cruz can take little solace from his vaunted delegate-wrangling operation even if he prevails there.

It turns out that delegates — like ordinary voters — are susceptible to shifts in public opinion. And as the gravitational pull of Mr. Trump's recent primary landslides draws more Republicans toward him, Mr. Cruz's support among the party's 2,472 convention delegates is softening, threatening his hopes of preventing Mr. Trump's nomination by overtaking him in a floor fight.