To increase production, spending must increase. People are out of work or worried about their jobs. So, no C increase . Business have a gloomy outlook and unused factories. So, no I increase .
Foreigners are in the same situation.
So no X increase . Only a G increase . Also, a T decrease yields the same effect. Lowering taxes leaves more money in the pockets of people and businesses who will increase C and I spending. During the Great Depression, incomes were already low and tax revenues scanty, so a T decrease would have been too small to be effective.