Do these cases of government debt and budget deficit indicate potential problems for the economy?

Does the size of the government's debt and the size of the budget deficit indicate potential problems for the economy in any of these cases?

1. The government's debt is relatively low, but the government is running a large budget deficit as it builds a high-speed rail system to connect the major cities of the nation.

2. The government's debt is relatively high due to a recently ended deficit-financed war, but the government is now running only a small budget deficit.

3. The government's debt is relatively low, but the government is running a budget deficit to finance the interest payments on the debt.

Well, the first two indicate government spending which circulates money in the economy leading to a higher GDP. The third one indicates a deficit not due to government spending. The third one would have more of an impact on the economy so I would say the third one would indicate what you had asked.

the third seems most likely because of the risk implication, as the gov is using a budget deficit to finance interest.