Short phrases only require short breaths. But complex sentences pose challenges for speakers who don't want to weaken points by stopping in the middle and gasping—however slightly—for air. You can control your need for air just as people train themselves to stay underwater for long periods.
Start by saying a short sentence first. Then add phrases one at a time while extending your endurance.
Practice: "This is the cow, with the crumpled horn, that tossed the dog, that worried the cat, that killed the rat, that ate the food, that lay in the house that Jack built." You can also use "The Twelve Days of Christmas." Each day you practice—and lengthen the sentence—your endurance grows.