Economic activity has benefits for society at large -- we get stuff out of it, and there's a feedback loop where more people with money in their pocket means more demand, which means more people employed, which means money in their pocket, etc.
Recessions are when the economy gets out of balance (historically inventory oversupply, more recently it tends to be financial meltdowns) and that feedback loop goes negative -- less money in pocket, so less spending, so less production.
Counter-cyclical spending is, according to economic theory, the one point in the cycle where the government should be encouraged to spend money like they're in vegas, up 50k and hanging at the strip club. Breaking this negative feedback loop is priority #1 -- debt can be paid back later, and if you've been breaking out your counter-cyclical toolkit, you've already lowered interest rates to near-zero so this is really cheap debt, 1% interest or lower -- if you produce any return at all, you've got a win in addition to the counter-cyclical effects.
Once you've decided to spend, you've got to decide how. Giving money to people in lump sums (which was in fact about 40% of the bill, the bill was 40% tax cuts) is fast and simple, so it certainly has a place, but keeping people in a job is far more effective because you create externalities. That job is producing something of value to the economy, that person is gaining skills/experience leading to future employability, and assuming that business is ok, their labor might lead to additional job openings at the same company later. These are all sustainable improvements that build on themselves and contribute back towards that positive feedback loop. Just spewing money out to people without any targeting whatsoever can only be a brake on recession -- it doesn't really help lay the foundations for the bounceback.