US officials have warned there could be big delays in getting visitor visas after new regulations begin in October.
All travellers may soon be fingerprinted on arrival in the US
Twice as many people are expected to ask for visas next year but there will be no more staff to process requests.
Travellers from the UK and other western European countries will lose the privilege of going to the US for up to three months without a visa.
From 26 October the US wants all new passports to contain a microchip with an array of personal data.
But the UK, among others, has said it will not be able to issue such passports before the middle of 2005.
Correspondents say that could mean hundreds of thousands of Britons having to apply for visas - with similar effects in other countries now served by the visa waiver programme who say the technology demanded by the US is simply not ready yet.
The BBC's Jon Leyne says US state department officials are describing the future situation as a "frightening prospect".