WASHINGTON—The Biden administration’s efforts to renew legislation that allows the U.S. to track the electronic communications of terrorists, spies and hackers overseas is facing an uphill battle amid increasing opposition from some members of both political parties and a looming end-of-year deadline.

For years, privacy advocates have criticized the law, but Congress renewed the legislation twice with broad bipartisan support. Fifteen years after it was first passed, a tool designed to track threats abroad has been caught up in domestic political controversies at home and is on the verge of dying—or being sharply curtailed—even as the U.S. faces renewed concerns about terrorism in the Middle East.