But the bare-knuckle, brawling style that the Tea Party brought to American politics, Mr. Brandon added, is still very much intact. And in Mr. Trump, the movement has found a champion who is temperamentally suited to its way of practicing politics — even if he cares little for its founding ideas.

One significant limitation to the Tea Party is the contradiction in its DNA: It was a mass uprising based on notions of small-government libertarianism that are popular with think tanks but not so popular with most Americans. And as Mr. Obama’s allies saw the movement, its outrage over the debt and deficit had another purpose: giving cover and a voice to those who wanted to attack the first black president — people who in some cases showed up at rallies waving signs with racist caricatures and references.

“If the worry about the debt was so all-encompassing, so crucial, we would have had President Mitt Romney,” said Rebecca Mansour, a former adviser and speechwriter for Sarah Palin, whose rallying cries like “Don’t retreat, reload!” offered catharsis to tea party-goers in the movement’s early days.

A decade ago, people were concerned with government debt and spending and what it came to symbolize: politicians who were unresponsive to their concerns and an economy that wasn’t benefiting most Americans. Those concerns are very much still present. “The big problems, what Elizabeth Warren would say are structural problems, were never addressed,” Ms. Mansour said.

Jenny Beth Martin, who helped found one of the largest national Tea Party groups, Tea Party Patriots, recalled an encounter with a Republican member of the House Appropriations Committee and his staff during the budget negotiations when Mr. Obama was still in office. That committee member told her, in effect: “Everyone else who comes into this office asks us for something to spend money on. And you guys come in here and you are the only ones to ask us to not spend money. And we don’t know how to handle that.”

“That was such an important moment,” Ms. Martin added, “because I realized we were asking for something they don’t know how to give.” At the height of its influence in 2011 and 2012, Tea Party Patriots was bringing in $20 million a year in contributions and employed 30 people, its tax records show. In 2017 it collected $4.8 million and had a staff of 15.

While the group opposed the spending deal that Mr. Trump signed, most of its solicitations for donations these days are either about Mr. Trump or issues that are broadly popular with conservatives. Recent subjects of its fund-raising emails have included condemnations of Robert S. Mueller III, the former special counsel, gun control laws, Big Tech, liberal judges. For $24.99 the group sells a T-shirt with a quotation from the president, “America will never be a socialist country.”