A Fort Worth lawmaker’s sit-in on the Texas House floor picked up steam late Tuesday as fellow Democrats flocked to her side for the second night of her round-the-clock vigil after she refused to allow a state trooper to shadow her until the chamber could vote on a new congressional map.

state Rep. Nicole Collier was inside the chambers, having spent a rumpled night there in a one-woman standoff against state Republicans.

When they returned Monday, Republicans insisted that Democrats have around-the-clock police escorts to ensure they wouldn’t leave again and scuttle Wednesday’s planned House vote on a new political ma...