Long before Donald J. Trump crashed their party, Republican strategists feared that Democrats had grown more skilled at running campaigns. Now they’re scrambling to keep from falling further behind.

Mr. Trump thwarted a large field of rivals for the Republican nomination by capitalizing on his celebrity, his ubiquitous television presence and his easily understood pledge to “Make America Great Again.”

Television ads, field organization and digital microtargeting had little to do with it.

But other candidates are unlikely to replicate that formula. Beaten twice by President Obama’s data-driven organization, some Republicans say their party needs to adjust its campaign techniques more rapidly to compete with Democrats, regardless of how Mr. Trump fares on Election Day.

“We are still dominated by a culture of people who did grow up in a non-cellphone age,” Michael Meyers, president of TargetPoint Consulting, told a gathering of campaign operatives in Washington last week. “We are ripe for disruption.”