He follows three high-profile Goldman Sachs alumni out the White House doors: Chief Strategist Steve Bannon, Deputy National Security Adviser Dina Powell and Communications Director Anthony Scaramucci.
Cohn was a surprising addition to the Trump administration.
"Congress can not be complicit as the administration courts economic disaster", said Sen.
Last week, the president announced his intention to impose tariffs on imported steel and aluminum, though "announcement" overstates what happened.
Liddell is now the White House's director of strategic initiatives and is said to be a key ally of Jared Kushner in an administration rife with internal feuds. "He is a rare talent, and I thank him for his dedicated service to the American people".
"The American aluminum and steel industry has been ravaged by aggressive foreign trade practices", Trump declared at a White House ceremony, surrounded by steel and aluminum workers holding white hard hats. The effect of Cohn's resignation and a number of other aspects will soon show its effects in the stock market.
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Trump has not made a firm decision, those briefed on the process said.
Cohn's departure has raised concerns about who within the White House will seek to temper Trump's nationalistic instincts. Navarro later said he was not on Trump's shortlist.
Since Trump moved into the White House, Cohn and other aides have restrained Trump from pursuing what they regard as protectionist policies. That has raised the possibility of whether Congress will block Trump's trade decisions. Special counsel Robert Mueller's investigation poses an existential threat to the Trump presidency, but lesser hazards corrode its day-to-day operations.
Congressional pressure instead might force Trump to revise his initial proposal to impose a 25% tariff on imported steel and a 10% tariff on aluminum.
While aides said Trump hopes to sign the required paperwork by the end of this week, aides continue to suggest that there may be changes of exemptions, a sign of possible flexibility within the nationalist agenda. But Liddell, the White House director of strategic initiatives, is seen as a front-runner to replace Cohn as director of the National Economic Council, they said. The European Union and other allies are targeting items that include orange juice from Florida, motorcycles from Wisconsin, and tobacco from North Carolina, all of which are politically important states.
Securing a greater balance in trade with China will also be hard if Trump resorts to punitive measures.
Canada, America's neighbor to the north, was its single-largest source of steel past year, followed by Brazil, South Korea, Russia, Mexico, Japan and Germany.