Let them first enforce existing regulation around the blatant unauthorized use of data (such as the creative output of artists, programmers etc.,) without explicit consent. For example, just like how the US Library of Congress receives a copy of each print publication for archival and reference purposes, Congress can enable the archival / storage of datasets for the purposes of AI research. Willing participants can deposit copies of their data sets (or URLs to source) and it would do more for AI research as a public good. The licensing terms could protect the rights of those who own copyrights on the datasets. There can even be commercial licenses enabled (already happens for legal documents such as court judgments ets.,).
If US Congress regulates too soon to constrain rather than enable, the tech companies would just setup shop in other jurisdictions where such regulatory hurdles don't exist.