That's $350,000 per job. About half of the 640,000 jobs from the $159 billion were as teachers, who earn a little over $40,000/yr. That means that about 11.4% of the stimulus money found its way into the hands of people who otherwise would have been unemployed, before taxes.
The argument against giving money directly to unemployed people is that then they wouldn't have an incentive to find jobs, resulting in inefficiency, as a large percentage of the unemployed-but-employable would remain idle.
Assume that the cost to society of a worker choosing not to work is about $40,000/yr in lost productivity. In order for distributing $348 billion directly to the unemployed to have less than 11.4% efficiency, it would need to motivate 7.7 million people to stay unemployed who otherwise would have found jobs. As there are currently only 15.1 million unemployed people in the US according to the US Dept. of Labor, I find this unlikely.
(This isn't a fair comparison, because the money "lost" by giving it to business owners is just redistributed, while the productivity lost by people not working is really and truly lost. But let's follow this idea through anyway.)
In fact, you could guarantee that this wouldn't happen, by giving the money to fewer than 7.7 million people. Give 3.48 million unemployed people $100,000 each. Once you've given them enough to motivate them to stop working, you don't lose any more productivity by giving them more. Giving people much more money than they are accustomed to, increases the percentage of it that they will spend. And if they don't spend it, they put it into a bank, where someone else will spend it. Either way, the stimulus money still flows to the business owners; it just goes through the unemployed first this way, causing a little inflation in exchange for giving a much larger share of the benefits of the stimulus to its alleged target population. You'll have provided a higher standard of living, for 3.5 times as many people, on top of your business stimulus.
Of course, instead of better schools, police forces, and road systems, you'd end up with an extra $348 billion worth of Playstations, movies, concerts, and internet porn.