Two dozen conservative groups, including the Club for Growth, FreedomWorks and the National Taxpayers Union, urged Trump to reconsider, writing in a letter that the tariffs would be "a tax on the middle class with everything from cars to baseball bats to even beer". The UK steel industry has said that tariffs would have a "profound impact" on their business and the British Prime Minister has voiced here concerns to Mr Trump about the move.
"What we're hoping is that the Canadian government will find a long-term solution..."
The proclamation signed by Trump ordering the tariffs do suggest some possible grounds for exemptions based off the specific reasons listed for excluding Canada and Mexico.
The signing ceremony for the proclamation issued at the White House was attended by several steel and aluminium workers, some of whom spoke of how excessive "dumping" of steel and aluminium imports had negatively affected their jobs and families.
"Of course this will have to go through the usual litigation process, either the WTO or the courts to see how this works", Cornyn said at an energy conference in Houston.
American steel and aluminium workers have been betrayed, Mr Trump added, but "that betrayal is now over".
Philip Levy, a former trade adviser in President George W. Bush's administration, said the flaw in Trump basing his tariffs on national security was that military allies could ask to be excluded, undermining the president's stated goal of protecting domestic steel and aluminum mill jobs.
While Mnuchin said that the tariffs will "definitely" be rolled out soon, both he and Commerce Secretary Wilbur Ross on Wednesday signaled the administration is open to exempting countries from the tariffs, including Mexico and Canada, depending on the result of ongoing Nafta negotiations.
"We're trying to balance protecting these industries, which are very important, with making sure we don't do undue harm to the economy", Mr. Mnuchin said Tuesday.
Only last month Trump went to Davos accompanied by Cohn, to reassure the business world that his "America First" policy did not mean America alone.
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If Trump does impose steep tariffs on foreign steel and aluminum, it will put the WTO in an awkward position.
The spokesman reiterated the secretary-general's offer to "do whatever he can to help facilitate the process". Most economists have questioned the benefits of tariffs compared to their economic costs, especially in light of the global competitive boost from the recently enacted Tax Cuts and Jobs Act.
Trump praised his top trade representative during his remarks March 8, and said Lighthizer would be responsible for negotiating with countries seeking additional exemptions from the aluminum and steel levies.
"We have the ability to adjust and adapt to a variety of market changes around the world and that will be our approach on this issue as well", the company added.
Republican Senator Jeff Flake has already introduced legislation to nullify the tariffs.
"Trade wars are not won, they are only lost", said Mr Flake, who a year ago announced that he would not seek re-election in 2018, meaning he is less susceptible to the President's frequent attacks than most.
"Congress can not be complicit as the administration courts economic disaster", the Arizona senator added.
Right now it is unlikely that the Republican-led Congress can muster up enough votes to block Mr Trump. They can acquiesce to Trump's tariffs, even though many of their donors hate them and they will hurt some of the GOP lawmakers' constituents, and create political opportunities for the Democrats.
"Exempting Canada and Mexico is a good first step, and I urge the White House to go further to narrow these tariffs so they hit the intended targets - and not United States workers, businesses, and families", House Ways and Committee Chairman Kevin Brady, who is a Republican, said in a statement.
The news on the economic front continues to be excellent.
But Trump has shown he wants more.