They called him a madman, a con man, a cancer and worse during an ugly nominating fight, but in the week since Donald J. Trump became the presumptive Republican presidential nominee, many of his former rivals and members of the party’s establishment are already softening on him.

Hard feelings are often short-lived in presidential politics, but the personal nature of this year’s race raised fears that unity would be hard to achieve. While a battered former Gov. Jeb Bush of Florida and a bruised Senator Ted Cruz of Texas are still keeping their distance from Mr. Trump, the recent outreach among others who assailed him for months has been swift and striking.

Perhaps the starkest example of this was Senator Lindsey Graham, whose personal cellphone number was read aloud publicly by Mr. Trump last year in a prank that set the schoolyard tone of the campaign. The Republican from South Carolina has regularly called Mr. Trump “the most unprepared person I’ve ever met to be commander in chief,” and he once likened backing Mr. Trump to being shot.

It appeared to be just a flesh wound, however, as the two men put their differences aside this week and spoke by telephone to discuss national security policy. Calling their 15-minute conversation “cordial,” Mr. Graham offered rare praise for Mr. Trump.