While alliances have been fluid in this White House, Mr. Kushner is joined by more centrist-minded advisers including not only his wife, Ivanka Trump, who now has her own West Wing office, but also Gary Cohn, the president’s national economics adviser, and Dina Powell, a deputy national security adviser, both veterans of Goldman Sachs.

Mr. Bannon’s closest ally is Stephen Miller, the president’s senior adviser for policy and the author of orders to temporarily ban visitors from certain predominantly Muslim countries. And although they were once at odds and still come from vastly different vantage points, Mr. Bannon has also maintained an alliance of convenience lately with Reince Priebus, the chief of staff closely associated with the Republican Party establishment.

In recent weeks, as Mr. Bannon has felt increasingly frustrated, Mr. Priebus has several times bolstered the chief strategist in discussions with the president, according to people with direct knowledge of the talks. In turn, Mr. Bannon has gone out of his way to praise his onetime rival’s performance.

Mr. Kushner and the others are said to be especially concerned about the geyser of bad headlines that have marked the president’s first two and a half months in office. They have resisted many of the more polarizing policy initiatives favored by Mr. Bannon’s side, including the travel ban and rollbacks of environmental regulation and of protections for transgender students, arguing that they undercut Mr. Trump’s election night pledge to be a president for all Americans.

On foreign policy, Mr. Kushner is more inclined toward intervention in the Middle East while Mr. Bannon would prefer that the United States remain as uncommitted as possible. Even as the president signaled this week that he might respond militarily to the chemical attack on civilians in Syria, Mr. Bannon has argued that American interests are better served by not getting drawn any further into the quagmire of a civil war.

From his point of view, Mr. Bannon describes the struggle in militaristic terms, vowing to associates that he “won’t give an inch.” He tells Mr. Trump that there is no political benefit to drifting even slightly toward the center on core issues like the Mexican border wall, immigration and the environment, while he argues against a large infrastructure spending package without a clear way to pay for it.

Mr. Bannon argues that it would be a fool’s errand to try to placate Democrats on Capitol Hill. That is a view shared by Mr. Priebus, a former chairman of the Republican National Committee. If Mr. Trump made a deal on health care with Democrats, Mr. Priebus told the president, it would jeopardize his chances of winning the Republican nomination in 2020, according to a person present for the conversation.