How would the US government mandate a non-US business do anything? They can't prohibit US citizens from buying from these companies without violating their own free-trade agreements. That'd be a bad idea, since 41% of the country's exports go to countries we've signed those treaties with.
I imagine the US government could just add said non-US business to an embargo list of some sort. Prevent them from doing any business whatsoever with US citizens.
I guess there's the open question of forcing foreign agents to collect and report IRS-friendly numbers. But it's not like taxing of import items is a new idea or a controversial one. The US government has been collecting duties for as long as it has existed.
