AP

When Commerce Secretary Wilbur Ross held up a can of Campbell's soup in a CNBC interview to make the case that the Trump administration's steel and aluminum tariffs were "no big deal," the canning industry begged to disagree — and they were hardly alone.

President Donald Trump's strong-armed trade policies have set off an intense scramble among industry groups, companies and foreign countries seeking exemptions from tariffs of 25 percent on steel imports and 10 percent on imported aluminum. The push comes ahead of an upcoming round of new penalties expected to be slapped on China by week's end.