It's more complicated than just "spending causes problems". People think of the government has a household and that's just a bad analogy cuz its very different; it's more like an investor.
Spending money is actually a type of investment. The government is betting that if it spends enough money, it will get the engine running again which will create more wealth than there was before. The problem with the stimulus is that it targeted a bunch of BS, to be frank. The type of spending that works during recessions is spending on infrastructure and defense manufacturing.
What happened during world war 2 is that the massive amount of spending we put into creating our military industrial complex shot us out of the depression. FDR had previously attempted to stimulate the economy. He was under pressure though, so he inevitably gave in to demands and tried to balance the budget. The effect? A recession admist the depression. However, by 1939, we were building up for war and the war spending drove us out of it.
The problem with government spending during bad economic times is that it's really hard to take the government out once its in. That's why we have our military industrial complex still in place today.
If the stimulus was enough and it actually works, what's probably going to happen in my estimation is that the government's size will increase permanently. This time, the increase will be too much for the government to sustain. some type of collapse will happen after that.