How Trump decides to proceed could drive the wedge deeper between the opposing sets of advisers. But successful negotiations with Congress on federal spending could help the two sides smooth things over.
Here are a few decision-points that could prove telling for the divide within the White House:
The White House and Congress have until April 28 to reach an agreement on funding the federal government and avoid a shutdown. Failing to strike a deal would amount to a major blow for Trump and his team, who entered office with GOP majorities in both the House and Senate.
While negotiations between Republicans and Democrats are still underway, an emerging deal would fail to fulfill a pair of Trump's campaign promises: It wouldn't defund Planned Parenthood and it would provide few dollars for the wall on the southern border.
That's a blow to conservatives, who have championed those issues and hoped to see them realized with Trump in the Oval Office. Instead of trying to convince conservative House Republicans to go along with the plan, the GOP leadership in the House will lean on Democrats to keep the government open.
For Trump, signing a bill that maintains funding for Planned Parenthood while lacking money for the border wall would be a blow for his conservative base -- who see Bannon as their advocate in the West Wing.
Alternately, if House conservatives find a way to scuttle the bill -- and the government shuts down -- Bannon could also catch the blame for not being able to bring along like-minded Republicans.
Paris Climate deal -- to stay or to go?
Trump has until late May -- before a Group of 7 meeting in Italy -- to decide whether to withdraw the United States from the Paris climate agreement, which President Barack Obama signed onto in late 2015. The decision will place into sharp relief the dueling factions within the West Wing, who disagree on whether the pact is legally binding or whether withdrawing would send the wrong signals to global allies.
Bannon, along with EPA administrator Scott Pruitt, have spoken against the deal. But Kushner is against withdrawing, and his wife, Trump's daughter and senior adviser, Ivanka, has said climate would be one of her top issues. Secretary of State Rex Tillerson has said withdrawing from the deal could erode faith in US leadership.
This week, Trump's top advisers plan to meet and discuss their recommendation on whether to withdraw.
"Senior officials will meet this week to discuss the options, with the goal of providing a recommendation to the President about the path forward," a White House official said Monday.
In either scenario, it's not clear how the US could uphold its commitments to the Paris climate accord. The US had committed to reducing its emissions by up to 28% from 2005 levels in a decade, but Trump signed an executive order in March scrapping Obama's Clean Power Plan, which was the lynchpin of the US strategy for reducing emissions.
April 29 is Trump's 100th day in office, the traditional milestone of progress for a new administration that Trump's administration is eyeing anxiously. Staffers met earlier this month to plot a branding strategy to sell the administration's opening stretch.
The focus of the meeting was salesmanship, but West Wing staff realize that news coverage of the 100-day mark will color Trump's own perceptions about his team has performed in the administration's early days.
That includes Bannon and Kushner, but also aides like chief of staff Reince Priebus, who has been combating rumors about his standing almost since assuming his role in January. What Trump regards as his successes versus his shortcomings could lead to new dynamics among his closest advisers.
Last week, Trump touted what will likely be considered his biggest victory thus far: confirming Neil Gorsuch to the Supreme Court.
"I got it done in the first 100 days," Trump said during a Rose Garden ceremony last week. "That's even nice. You think that's easy?"