"I think he's wrong on a lot of things", said Senate Finance Committee Chairman Orrin Hatch of Utah, who opposes the tariffs.
Cohn's position with Trump had been tenuous since last summer, when Cohn rebuked the President over his comments about a white supremacist rally in Charlottesville, Virginia. Jeff Flake, (R-Ariz.), who vowed to file a bill to nullify Trump's proclamation.
During his stay at the White House, Cohn led coordination of Trump's pro-growth domestic and global economic policy agenda, including the passage of historic tax cuts and reforms in December 2017.
The European Union has promised tariffs on items from steel to peanut butter, bourbon and denim - most of which are produced in states that Trump needs to win re-election.
In a press briefing Wednesday with reporters, White House press secretary Sarah Sanders said she will not be offering a list of contenders.
Mr Cohn stepped down on Tuesday, having lost the bruising battle over the direction of Mr Trump's trade policy. And the year began with the departures of deputy national security adviser Dina Powell as well as Cohn's deputy on the National Economic Council, Jeremy Katz. Trump asked Chung about a recent meeting with the North Korean dictator.
The president has always wanted a prominent business figure to oversee the council, according to people who have spoken with him.
President Donald Trump's sharp turn toward protectionism over the last week has been a victory for advisers such as Peter Navarro and Wilbur Ross, who had been pushing the president to slap tariffs on foreign goods. Trump didn't back down and is set to sign the tariffs into law on Thursday.
The EU's top trade official Cecilia Malmstroem insisted the entire bloc "should be excluded" from the tariffs as a "close ally", vowing to "seek more clarity" from Washington.
Securing a greater balance in trade with China will also be hard if Trump resorts to punitive measures. At another point, during a meeting with steel and aluminum executives, Trump urged Cohn to engage in a debate with U.S. Steel CEO Dave Burritt, according to two people familiar with the exchange and not authorized to discuss it publicly.
Trump mentioned the possibility of tariffs on the campaign trail.
"Strategically, we still really like worldwide and emerging markets, but when you have asymmetric risks, that makes us a little cautious on non-U.S. assets for now", given that markets have not yet priced in the possibility of more protectionist policies, he said. "This is not a conventional president and because of that we're getting results we wouldn't have otherwise seen".
Advisers and supporters were caught off guard recently when Trump appeared to embrace gun control measures at a freewheeling roundtable with lawmakers in the wake of a Florida school shooting. These moves suggested that Trump would be willing to modify his hardline "America First" trade policy into "America first, but not alone".
Daniel Pinto, a co-president at JPMorgan Chase & Co, said in an interview with Bloomberg on Thursday that the US equities could fall by between 20 and 40 percent over the next three years if a global trade war breaks out.
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