Volunteers turned away scores of supplies as a steady stream of local families marched towards the city's storm shelters Monday, delivering hundreds of home-cooked meals, closets full of clothes and truckloads of toys for families fleeing the ravages of Tropical Storm Harvey.

The surplus supplies were sent to smaller shelters spread throughout the region, as well as a central distribution center preparing for the city's convention center to receive 5,000 people Tuesday.

"I brought a box of five warm, cooked chickens from home," said Dallas resident Colleen O'Connor in an interview Monday. "Because I thought people were getting tired of eating canned soup constantly."

O'Connor was one of the Dallas natives who made her way to Walnut Hill Rec Center, now filled to capacity with 300 people since Friday.

The shelter will operate at least through Friday, with Dallas Red Cross officials then evaluating whether to keep the shelter open into the weekend.

"We have families here from as far as Corpus Christi," said Brenda Reed, a Red Cross shelter coordinator. "We are like a family here, with people living at the shelter helping us sort through donated clothes, and keeping the place clean like their own homes."

The rec center and parking lot at Walnut Hill will be home for the Poullard Family, a family of 11 that left Beaumont, T.X. Thursday.

"There is stress with the kids, the grandbabies and everything," said Hilary Poullard as he stood next to his family's caravan. "We're just trying to make it."

Poullard traveled 300 miles to safety with his mobile food stand in tow, the small cooking business he owns with his wife. They cook shrimp and hotdogs at summer baseball games, and took their chrome cooking stand in case they were trapped on the road.

"We have a little bit of food left, and even birthday cake," Poullard said. "It was my wife's birthday yesterday, so we celebrated that and celebrated escaping Harvey."

Volunteers from the Red Cross and the city of Dallas Community Emergency Response Team are working 12 hour shifts at the shelter, as well as finding places for children who need to attend school, and serving as Spanish interpreters.

"We were ready for this," Reed said. "This is my seventh time running a shelter for the Red Cross, and I can say the spirit of Dallas is keeping us, keeping everyone going."