"Tariffs are very damaging," Norquist said while appearing on "The Daily Briefing." He told Fox News host Dana Perino that tariffs acted as taxes on the United States.
"Well, the challenge is that tariffs are taxes," he said. "They're taxes on American consumers. We pay tariffs imposed by the United States, not China, not other countries."
"We also have challenges that when our companies import goods and services for us to export, it makes our products more expensive, not just for Americans, but when we try and compete," he said.
Norquist, who leads one of the most prominent organizations opposing tax increases, seemed to highlight the tension between populist and more libertarian segments within the Republican Party.
Despite some conservatives' hesitance, President Trump pursued an aggressive "America First" agenda that included punishing China for what the president described as unfair trade practices.
Trump's administration, amid stalled negotiations with China, began raising tariffs to 25 percent for $200 billion of Chinese goods early in May.
Sen. Rand Paul, R-Ky. warned on Sunday that if Trump continued levying tariffs on China, it could backfire in the form of a trade war.
"I still have advised the administration: get this done, because the longer we're involved in a tariff battle or a trade war, the better chance there is we could actually enter into a recession because of it," he said.
Voters, according to a Fox News poll, credited Trump for a good economy but, by an 11 point margin, said they thought increased tariffs would hurt the economy rather than help it.