Even the typically Republican-aligned U.S. Chamber of Commerce is pushing back on the White House's trade tariff policies.

On Monday, the country's largest business group launched an online campaign against President Donald Trump's hardline stance on trade, which his press secretary described as a way to "create a fair playing field" for U.S. businesses.

"We think trade works for the American economy and tariffs don’t," John Murphy, the Chamber of Commerce's senior vice president for international policy, told CNBC's "Closing Bell" on Tuesday.

"There is, as a consequence of the tariffs that the United States is putting in place, a wave of retaliation that’s coming against American exports" from trading partners like Canada to the tune of $75 billion, Murphy said.

Murphy noted that additional retaliatory tariffs from Mexico and China would come into effect later in the week. Mexico plans to raise existing tariffs on unprocessed U.S. pork to 20 percent from 10 percent on July 5, and China will place a 25 percent tariff on U.S. soybean exports on July 6.

The Chamber of Commerce's campaign website, thewrongapproach.com, tracks the impact of retaliatory tariffs on U.S. exports from each state. The initiative is also enlisting 2,000 local and state chambers of commerce to call on Congress to review the "real costs" of the tariffs, Murphy said.

"Every state in the union is feeling a local impact from this global trade war," Murphy told CNBC. "Tax reform, regulatory reform have delivered benefits for the economy. We’re worried that that could be put at risk by these tariffs.”

Some of the hardest-hit states include Texas, where $3.9 billion worth of exports including pork and whiskey are under threat from retaliatory tariffs, and Alabama, where $3.6 billion worth of exports are threatened by tariffs on U.S. goods from China, the EU, Mexico and Canada.

On Tuesday, Trump again slammed motorcycle maker Harley-Davidson on Twitter for moving some of its operations overseas to try to evade retaliatory tariffs on the motorcycles it ships to Europe.

“Now that Harley-Davidson is moving part of its operation out of the U.S., my Administration is working with other Motor Cycle companies who want to move into the U.S. Harley customers are not happy with their move - sales are down 7% in 2017. The U.S. is where the Action is!,” the president wrote.

But for Murphy and the Chamber of Commerce, threatening companies whose businesses largely rely on exports was not the most constructive strategy in bringing trade to a fair playing field.

"As a general rule in business, you take care of your customers, and especially your best customers," the policy expert said. "And it so happens that American allies like Canada, Europe, Mexico – these are our largest markets in the world. And for us to initiate a trade war against them is not good for American companies that depend on exports. About 40 million American jobs depend on trade, and it’s principally with those markets."

Shares of Harley-Davidson ended Tuesday's shortened trading session up 0.8 percent. The major averages slid, however, unable to sustain an advance as trade tensions rose.