Stephen K. Bannon, President Trump’s former chief strategist, in October in Arizona.

WASHINGTON — Enthusiasm for Stephen K. Bannon’s plans for a fiery Republican revolution had already been fading among some of the donors and candidates he was relying on to upend the party’s establishment.

But Mr. Bannon’s provocative remarks about President Trump and his family, reported in a new book now scheduled to be released this week, and Mr. Trump’s angry response, further alienated some of Mr. Bannon’s most important backers — including the family of the hedge fund magnate Robert Mercer — leaving Mr. Bannon confronting the possibility of a dire fate for a publicity-hungry provocateur: political irrelevance.

The Mercers were blunt on Thursday in cutting the cord, reiterating support for Mr. Trump while disavowing Mr. Bannon’s remarks and disowning his political endeavors. “My family and I have not communicated with Steve Bannon in many months and have provided no financial support to his political agenda, nor do we support his recent actions and statements,” Rebekah Mercer, Mr. Mercer’s daughter, said in a statement. “I have a minority interest in Breitbart News and I remain committed in my support for them.”

The reference to Breitbart seemed an implicit threat. Mr. Bannon is chairman of Breitbart, and many staff members there believe there is a strong chance he might lose the job, though he was dismissive of that possibility on the site’s daily editorial conference call on Thursday night, according to one person with knowledge of the call.

Mr. Bannon’s predicament highlights a stark reality in American politics, unchanged even after Mr. Trump’s convention-defying victory: The influence of even the most influential political strategists is inextricably linked to the donors behind them and the politicians in front of them.

“If Trump is openly breaking with him, that dramatically lowers his capital,” said Dan K. Eberhart, an Arizona oil investor and Republican donor who has spoken to Mr. Bannon about his plans to build an antiestablishment political operation. “He is a strategic thinker, and a lot of the things he said make sense, but this stuff from the book — I’m not going to defend that.”

Mr. Bannon has never been bashful about his ambitions — or his belief in his ability to bounce back. When he was fired from his position as Mr. Trump’s chief strategist in the White House in August amid an uproar over Mr. Trump’s less-than-full condemnation of a white supremacist rally in Charlottesville, Va., Mr. Bannon predicted that he would become even more influential on the outside.

Mr. Bannon proclaimed that he would stage a revolt against Senator Mitch McConnell, Republican of Kentucky and the majority leader, recruiting primary race challengers who could defeat incumbent Republican senators and remove Mr. McConnell from his post. But building and sustaining costly infrastructure is difficult, especially for antiestablishment crusades like the one envisioned by Mr. Bannon, who in a speech at a September rally for Roy S. Moore, the Alabama Senate candidate, warned the Republican establishment and its donors that “your day of reckoning is coming.”

As significant, Mr. Trump, loyal to only a party of one and hungry for legislative success, was never committed to aiding a coup against congressional Republicans. Indeed, Mr. Trump effectively sided with the party establishment by helping to orchestrate his former aide’s political banishment, making Mr. Bannon the fall guy for an embarrassing string of political setbacks, most notably Mr. Moore’s defeat.

His associates said he was planning a political nonprofit group called Citizens of the American Republic that would spend between $25 million and $30 million — though some advisers predicted a budget as large as $100 million — to seed the primary campaigns. Half the budget was slated to be spent on voter mobilization efforts on the ground in targeted districts for months leading up to elections, with the other half going toward advertising, according to people familiar with the plan. While Mr. Bannon publicly bashed the Republican donor class, he spent months quietly courting some of the deepest pockets on the right.

Mr. Bannon discussed his plans in grandiose, but vague, terms in a series of meetings with donors, including the Las Vegas casino magnate Sheldon G. Adelson; a Chicago Cubs owner, Todd Ricketts; and a Home Depot founder, Bernard Marcus.

While Mr. Bannon boasted that he was turning donors against Mr. McConnell, some of the donors who talked to Mr. Bannon say he appeared to lack the organization to effectively raise and spend their money. For…