It is true that the cause of the budget deficit really matters since the effect the cause may have differs. Lower taxes will lead to a budget deficit but the citizens will feel encouraged to work since they are only contributing very little amount to the government funds through taxes. High taxes make people feel discouraged to work for they loose much of their income in the name of taxes. Increased motivation to work will lead to increased income and thus increased spending and further increased GDP, economic growth.
Other effects like increased defence spending and more job-training programs will not have a positive effect on the GDP growth but will only lead to the negative effects of budget deficit in the economy at once.