Republicans put down a right-wing revolt to push a three-year renewal through the House, but the Senate appeared likely to opt for a 45-day punt ahead of a Friday expiration.
Prosecutors accused Rubén Rocha Moya, the governor of Sinaloa state, and other Mexican officials of a yearslong conspiracy to protect the powerful cartel.
The case deals with Temporary Protected Status for hundreds of thousands of Haitians and Syrians but could have implications for more than a million from troubled nations.