Rising water has forced many in Poplar Bluff from their homes. Commerce and Benton were also affected.
The new legislation would give dog breeders more time to comply with the regulations passed in November.
Tuscaloosa Mayor Walter Maddox says sections of the city have been destroyed and its infrastructure has been decimated.
An emergency official says 10 more storm-related deaths have been confirmed in an Alabama county, bringing the regional death toll to 64.