I don't necessarily think we need to dump money into the supply side either. Targeted tax cuts, especially payroll tax cuts, are good to help businesses retain employees, but the main thing one can do with a recession is wait it out. Other helpful things include TARP-like programs and bank bail-outs and loans to help keep major institutions from going under. But the problem with artificially creating demand, whether by tax cuts or by government spending money, is that this demand is inelastic. When the spending stops, the economic stimulus stops. We saw that this time, and we saw that in the Great Depression, where unemployment rates rose each time the government tried to cut its stimulus spending. Only the war had any success at ending unemployment.
As far as tax cuts stimulating hires, this works two ways. First, when a business receives a tax rate cut it now has more profit flowing in. It can use some or all of this extra income to hire new people, which it will hopefully only do if management sees a way to increase revenue and profit. Second, it can bank that extra money and save it up for hard times (not a hiring stimulus but helps prevent more unemployment from business failure) or a capital investment project. If the former, another business can borrow that money for its own investment. (Even in the hardest of times there are people with good ideas to try, often because they've lost other employment.) If the latter, it may stimulate employment directly (purchase of goods and services) and indirectly (people who get paid purchase other goods and services.) The bonus of a tax cut is that much less overhead is involved to not take something than to take it and redistribute it.
Something like the Great Depression may call for things like labor programs, but we should be clear: we aren't stimulating the private sector, we're supplanting it.