A Republican law signed by President Donald Trump in December created new taxes for corporations that have shifted their profits offshore for years. But unlike other provisions in the bill, these international changes don't set a floor on annual gross receipts for when they kick in -- meaning Baldwin, who owns an industrial design company in Bristol, U.K., is on the hook even though he says his business has never made more than $100,000 annually.

The two taxes U.S. expatriates who own businesses abroad are most concerned about: a one-time repatriation levy of as much as 17.5 percent on old foreign profits and an annual levy called Gilti -- or global intangible low-tax income -- on foreign profits going forward.

"It's terrifying," said Baldwin, who added that he's had trouble finding a local tax attorney who even understands the new law. "It's just gotten so complicated. I feel like I have this burden that no one else has."

The tax changes are likely to convince some that it's no longer worth keeping their U.S. citizenship, according to Nora Newton Muller, who helps run the tax committee for the Association of Americans Resident Overseas. Other U.S. citizens, who haven't been paying U.S. taxes but are thinking of becoming compliant, might decide just to stay off the radar, she said.