About once a week over the past few months, aides for a bipartisan group of four Senate lawmakers have huddled in Capitol Hill offices to discuss what data privacy legislation in the U.S. should look like. They have a long way to go. One area of debate, said people close to the negotiations, is defining what consumer privacy means.

Disagreement over what constitutes personal information is one of the bigger hurdles that lawmakers will have to overcome in order to craft legislation that has a chance of being passed by Congress. But those close to the talks said the fact that a working group is holding meetings—an unusual occurrence in today’s polarized political climate—suggests that a legislative deal is possible.