His company at the time, Giles Parscale, took in more than $90 million from the campaign, the bulk of which went to online advertising — a sum that enraged Mr. Trump, at least before he won. Since then, Mr. Parscale’s new company, Parscale Strategy, has received six- and seven-figure payments by the Trump campaign, the Republican National Committee and the super PAC supporting the president.

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It is not clear how much money goes to Mr. Parscale directly; he maintains it is a small percentage.

None of Mr. Parscale’s critics were willing to speak on the record, a reflection of the power that he now wields. By contrast, top Republicans wanted to demonstrate support: The Republican National Committee chairwoman, Ronna McDaniel, said she was in lock step with him, and Representative Kevin McCarthy of California, the No. 2 House Republican, called himself a “big fan” and said that Mr. Parscale had shown it was time to abandon the orthodoxy of how campaigns should be run.

He tends to think in headline-making concepts, but sometimes Mr. Parscale has failed to consider the potential problems of an unconventional approach. When Roseanne Barr was fired from her ABC show over a racist Twitter post, Mr. Parscale mused about the possibility that she be invited to appear alongside Mr. Trump at his campaign rally later that night. Others quickly rejected the idea. When the acrimonious relationship between Mr. Trump and his attorney general, Jeff Sessions, reached one of its lowest points, Mr. Parscale jumped into the fray on Twitter, denouncing the cabinet secretary in deeply personal terms and calling for his dismissal, to the dismay of some White House officials.

Yet Mr. Parscale also sees the benefits at times of a more conventional approach. He was unnerved by Mr. Trump’s recent Twitter post describing Stephanie Clifford, the pornographic film star known as Stormy Daniels, as “Horseface,” according to several people. And Trump allies say Mr. Parscale, like his boss, is far less confrontational in person than the Twitter persona he has created.

Mike Shields, a veteran Republican strategist and a former chief of staff of the Republican National Committee, cautioned that the political establishment was making a mistake by waiting for Mr. Parscale to slip up.

“People in the political sphere are going to underestimate him, and that really benefits him,” Mr. Shields said.