HOUSTON (AP) — With its flood defenses strained, the crippled city of Houston anxiously watched dams and levees Tuesday to see if they would hold until the rain stops, and meteorologists offered the first reason for hope — a forecast with less than an inch of rain and even a chance for sunshine.

The human toll continued to mount, both in deaths and in the ever-swelling number of scared people made homeless by the catastrophic storm that is now the heaviest tropical downpour in U.S. history.

The city's largest shelter was overflowing when the mayor announced plans to create space for thousands...