We know from looking at second quarter GDP that about $30 billion of the $168 billion stimulus was spent, and that had an overall positive effect on consumption. But the question is, what happened to the rest? The answer is, it went into savings. Take a look at the chart of personal savings below.
It ballooned to $285 billion in Q2, mostly because of the money the government sent out to people. So the stimulus was far from a "one-shot-deal" as many like to say. It remains in the economy like potential energy, and over time, it will likely be spent. Even when it is spent, it still won't go away. Instead, it is transfered from consumers to firms, who then hire, spend and invest themselves and the cycle continues. Think of it like a stone being tossed into a still pond. The splash creates ripples that start off big and continue in a diminishing fashion over time. Even though we don't see them after a while, their effect on the water is still occurring.