Step on the accelerator with driverless vehicles and you scare off regulators and the public, but hit the brakes and you lose financial backers. It won’t be an easy balance for Cruise to strike as it looks for a route out of today’s crisis.

The autonomous-taxi venture 80%-owned by General Motors has lost both its co-founders since Sunday, including Chief Executive Officer Kyle Vogt. The resignations, which capped a tumultuous few weeks since the suspension of Cruise’s autonomous-driving permit by the California Department of Motor Vehicles, might make it easier to convince regulators that the business can make a fresh start.