Arizona Sen. Jeff Flake, a Republican, said he plans to introduce legislation next week to nullify the tariffs though he has acknowledged that finding the votes to stop the president's actions could be hard.
Top Wisconsin Republicans are not on board with President Donald Trump's steel and aluminum tariffs.
In a statement, McConnell said he was "concerned about the scope" of the tariffs and their impact on the USA economy.
"I think there's a good chance that we will nullify the tariffs", he told reporters.
"Trade wars are not won, they are only lost", he said in a statement.
The news of Flake's bill comes just one week after President Trump announced he would place 25 percent tariffs on imported steel and 10 percent tariffs on aluminum from all countries that send metal to the U.S.
Republicans worked frantically, without success, for days to publicly and privately urge the administration to back down or at least narrow the tariffs.
Several Republican senators indicated earlier this week that they were willing to move forward with legislation to counter the president if he pressed forward with the financial penalties.
"We urge the administration to take this risk seriously", Donohue said. "If I have to hold oversight hearings, I'll do that as well". Trump made the move under section 232 of the Trade Expansion Act of 1962 after extensive Department of Commerce research into the issue.
"I'm not sure there are any winners in trade wars", said Johnson, who ran a plastics manufacturing business in Wisconsin before being elected to the Senate. Some of them will be mildly helped by the president's tariffs.
The Senate's top Democrat, Charles Schumer of NY, said Trump's instincts on trade were right. The former real estate developer said politicians had for years lamented the decline in the industries, but nobody was willing to take action.
Flake, an Arizona conservative who has frequently feuded with Trump, said that Trump's "so-called "flexible tariffs" are a marriage of two lethal poisons to economic growth - protectionism and uncertainty".
"China has been rapacious about trade", Schumer said on the Senate floor Thursday. That scenario, Tom Donohue said, would endanger the economic momentum from the GOP tax cuts and Trump's rollback of regulations.
But "the haphazard way these tariffs were put together has caused the policy to miss the mark", Schumer said.