For corporate executives and Wall Street investors worried about President Donald Trump's positions on import tariffs and immigration and his penchant for sparking confrontations with global leaders, there is a key power struggle to watch inside the White House.

The key player, and the great hope for free traders and those who believe well-regulated but significant immigration is a key driver of economic growth, is National Economic Council Director Gary Cohn, former president of Goldman Sachs.

Cohn's fingerprints were all over Trump's rollout Friday of an executive order to loosen financial regulation and review the Department of Labor's fiduciary rule for brokerage advisors. He was there for the signing and lauded the moves in a series of interviews.

But the big question is not the extent to which the former Goldman Sachs president will influence financial regulatory policy. That's already pretty clear.

Cohn and Treasury secretary nominee Steven Mnuchin will drive financial deregulation along with House Financial Services Chairman Jeb Hensarling. Their success will determine whether the huge rally in bank stocks since the election is justified.

The more critical and long-term question for executives across multiple industries is whether Cohn will emerge as a powerful countervailing economic force to temper Trump's instincts toward protectionism. To pull this off, Cohn will have to nudge Trump himself while also muscling out Steve Bannon and Stephen Miller as well as to lesser degrees Trump advisor Peter Navarro and Commerce secretary nominee Wilbur Ross.

If anyone can pull this off, it's Cohn, a powerful personality not known to be shy about making his views known. He has an added bonus in his favor: He came into the Trump orbit through Jared Kushner and Ivanka Trump, critical advisors to the president. Those inclined to Cohn's worldview inside the administration believe the former Goldman banker will eventually win the day. Some even mention him as a potential future chief of staff or shadow chief of staff.

But nothing is for certain in Trump-world and Cohn will come up against some skilled infighters. And it's clear from his tweets (and from his campaign) that Trump himself has a strong mercantilist view of trade where one country wins and another loses. Changing that to a trade as win-win view will be extremely challenging. But Cohn has powerful allies, including former Goldman executive Dina Powell.

Cohn may also benefit from all the early press Bannon, who is on record with a desire to bring down the entire American system, is getting. Trump, who doesn't like to be outshone by anyone, is already showing signs that he is chafing at arguments that Bannon is really running the White House.

Bannon, not Trump, appeared on the latest cover of Time magazine as the power behind the throne. And a New York Times story on Sunday described Trump as essentially hoodwinked into putting Bannon on the National Security Council through an executive order.

That story sparked a strong reaction from Trump on Twitter on Monday morning. "I call my own shots, largely based on an accumulation of data, and everyone knows it. Some FAKE NEWS media, in order to marginalize, lies!" Trump tweeted.

The president directed his fire not at Bannon but at the Times, a favorite target of the new president who appears to hate-read the paper pretty regularly.

But if Cohn is to emerge as a powerful influence on Trump, pushing him away from tariffs and major moves to deport current undocumented immigrants and shut the doors to new ones, then he could capitalize on the president's unhappiness with Bannon's high profile.

The betting line among people both outside and inside the administration is that if the White House keeps running into big PR headaches and massive protests then an early shake-up will come among the president's top staff.

For companies and investors who like Trump's plans for tax cuts and regulatory relief, the hope is that when the shake-up comes, hard-line voices like Bannon and Miller will be marginalized and more moderate, business-friendly advisers like Cohn, Powell and current chief of staff Reince Priebus will emerge with stronger hands.

—Ben White is Politico's chief economic correspondent and a CNBC contributor. He also authors the daily tip sheet Politico Morning Money [politico.com/morningmoney]. Follow him on Twitter @morningmoneyben.

