Donald J. Trump knew that JD Vance could take a punch. But during their first week together on the campaign trail, the former president wondered just how many hits his new running mate could absorb.

The volume and velocity of attacks from Democrats stunned even Mr. Trump. He was unaware of the most incendiary remarks that opponents were rapidly unearthing from Mr. Vance’s past, and the former president told allies that he was troubled by the idea that more comments would come to light as Democrats savaged his heir apparent as weird and anti-women.

A month later, polls show that the number of Americans who dislike Mr. Vance continues to grow — but Mr. Trump could not be happier.

The reason: Mr. Vance’s relentless pace of full-throttle performances as Mr. Trump’s well-trained attack dog has pleased the former president and instilled a sense of stability inside a campaign still shaken by President Biden’s sudden exit from the race.

Mr. Trump had instructed his young sidekick to fight forcefully through those initial attacks, and later said Mr. Vance’s execution exceeded his expectations, according to three allies who insisted on anonymity to discuss private conversations.

In a quintessentially Trumpian display of bravado, the former president has privately praised Mr. Vance by comparing himself to Vince Lombardi, telling people that his eye for political talent was now on par with the Hall of Fame football coach’s ability to find Super Bowl-caliber players.