The law is meant to ensure Americans cannot use hidden trusts overseas to evade taxes, a goal that is widely applauded. But critics say that it amounts to gross legislative overreach, and that the $8 billion the Treasury expects to reap in taxes owed over 10 years pales next to the costs it will impose on foreign institutions. Those entities are being asked, in effect, to pay for the cost of tracking down American tax evaders.

The law demands that virtually every financial firm outside the United States and any foreign company in which Americans are beneficial owners must register with the Internal Revenue Service, check existing accounts in search of Americans and annually declare their compliance.

Noncompliance would be punished with a withholding charge of up to 30 percent on any income and capital payments the company gets from the United States. Under the law, for example, if Deutsche Bank, having agreed to register with the United States authorities in compliance with the law, were to transfer $25 million to a noncompliant Polish bank, Deutsche Bank would be required to withhold part of that sum, transferring it to the I.R.S. The Polish recipient would then have the option of challenging that withholding by filing an American tax return, claiming the money, despite not being an American citizen.

In practice, tax experts say costs like that might drive the Polish bank out of business.

“They’re trying to force every financial institution in the world to sign onto this regime,” said Denise Hintzke, who heads the global tax compliance initiative at Deloitte in New York.

Financial institutions outside the United States also say that the law’s costs will be imposed overwhelmingly on them, giving a competitive advantage to United States rivals.