Theodore Roosevelt did NOT create the New Deal. You are confusing two different US Presidents; Theodore Roosevelt with Franklin D. Roosevelt of the 1930's and 1940's. Franklin Roosevelt created the New Deal. Theodore Roosevelt created the "Square Deal".
Some of the major public works projects built during the New Deal were the Hoover Dam, the Lincoln Tunnel in New York City, and the Triborough bridge in New York City. The New Deal was created by Franklin Roosevelt.
The New Deal created a social safety net so not as many people would fall through the cracks and into extreme poverty. Additionally, the New Deal increased the velocity of money, kickstarting the economy after the Depression.