Large-scale data is an essential component of machine learning as demonstrated in recent advances in natural language processing and computer vision research. However, collecting large-scale robotic data is much more expensive and slower as each operator can control only a single robot at a time. To make this costly data collection process efficient and scalable, we propose a novel assisted teleoperation system, which automates part of the demonstration collection process using a learned assistive policy. The assistive policy autonomously executes repetitive behaviors in data collection and asks for human input only when it is uncertain about which subtask or behavior to execute. We conduct teleoperation user studies both with a real robot and a simulated robot fleet and demonstrate that our assisted teleoperation system reduces human operators' mental load while improving data collection efficiency. Further, it enables a single operator to control multiple robots in parallel, which is a first step towards scalable robotic data collection.