Among those calling for new federal laws is Apple chief executive Tim Cook, who recently praised GDPR and called for an equivalent to be passed in the US as soon as possible.
However, it seems, Americans are already taking action to protect themselves, according to the study carried out by SAS.
The majority (66%) of respondents have taken steps to secure their data, such as changing privacy settings (77%), changing or not accepting cookies (67%), declining terms of agreement (65%), deleting an app from a mobile device (56%) or removing a social media account (36%).
Meanwhile more than a third of survey participants (38%) reported using social media less often because of data privacy concerns.
Of survey participants who think the US needs more data privacy regulation, a large majority (83%) would like the right to tell an organisation not to share or sell their personal information, while 80% also want the right to know where and to whom their data is being sold.
In addition, 73% said they would like the right to ask an organisation how their data is being used, and 64% would like the right to have their data deleted or erased.
SAS global lead for GDPR Solutions Todd Wright said: "The survey results clearly show that consumers value their data privacy and are greatly concerned about potential misuse. Companies need to reexamine how they handle data and analytics in all aspects of the business.
"It's clear that in this age of increased data privacy concerns, even without a more stringent data privacy law in the US, organisations that treat their customers' data with care will be rewarded, and those that don't risk the loss of reputation and customers."