It seems a lot of the time you have people supporting increased government spending arguing against people supporting tax cuts for the rich. However little attention is given to the 'third way' - tax cuts for the poor (and/or tax hikes on the rich).
Firstly, the need for such actions: When an economy is in a recession, it has lots of unused capacity - just glancing at the unemployment rate will tell you as much, since it goes up during a recession. Since recessions are short term, if demand can be boosted up you can get the economy back near full capacity, generating far more money, and meaning that most if not all the pain from the recession is taken away. Confidence will also be boosted, businesses can plan better meaning better investment and in turn better growth, the vicious 'demand falls so fire workers to cut costs so demand falls further' cycle and others will be prevented, and all in all it's generally a good idea if you can manage it.
Secondly, how to take such actions? You basically have the choice between fiscal policy and monetary policy. The basic monetary policy tool is interest rates - cut interest rates and you make debt cheaper->people borrow more, they spend that money, and it boosts demand. Given the current situation that's not really working though, and interest rates can't be cut any further.
On the fiscal side, you have increased government spending as an option for boosting demand, and tax cuts as an alternative - that's what this post will focus on. The government can boost demand itself by spending money in various areas (see for example much of Obama's recent spending plan). This runs into some problems though, because the government isn't exactly the most efficient of entities (no incentive to make a profit, and it's run by politicians who aren't all exactly 'whiter than white'). They also lack perfect knowledge of everything, and hence will likely waste some of the money they spend. However it won't all be wasted, and a big splurge in government spending would (all else equal) boost demand.
An alternative to this is for the government to cut taxes on the rich and businesses. The idea is that those rich people will then have more money, they'll spend it, and/or invest it, hire more workers (in the cases of businesses), who will in turn spend the money they get, and you get the 'trickle-down' effect. Unfortunately this too suffers it's problems - the more affluent people are more likely to save money they receive from tax cuts than the poorer people (which makes sense - the poor people will struggle to get by, and so may well have necessities or near-necessities they'd spend their money on. They may also not be so prone to financial planning and so might not realise the value of saving some money 'for a rainy day'). Similarly tax cuts don't provide that great a direct incentive for businesses to hire workers - workers are an expense and so you get tax relief on money spent on them. Hence you'd only be hiring workers if you'd expect them to make you a profit. Taxes won't affect that, all they'll change is the amount of profit you make (not whether you make it or not). In fact the biggest thing to watch out for is just making sure the tax rate doesn't rise so high relative to other countries that businesses just move to those other countries. The US is hardly in such a position though, with low effective tax rates relative to many other developed economies, and also due to it's economic(and geographical) size that means even with high tax rates plenty of businesses would still operate because there'd still be money to be made.
Another argument for tax cuts on the rich is that if you cut taxes, they earn more per hour they work, and so working an extra hour becomes more attractive compared to the alternative of relaxing, and so they'll increase the amount they work. That has two key problems though. Firstly in the current climate, increasing capacity (which that would do) isn't needed since you'd still need the demand to make use of that capacity. Furthermore, with rich people you can actually end up in some cases with a tax cut decreasing the amount of hours they'll work, and similarly a tax increase causing them to increase the hours they work. The reasoning is that once a rich person hits a certain level of income, they may well have everything they really want, and so spending time relaxing will be much more valuable. Hence if they get a tax cut, they can earn that desired level of income by working fewer hours, thus increasing the time they have to relax. Similarly if taxes get increased, they may want to work more to maintain that level of income - in economic terms it's known as the backward bending supply curve of labour.
So then we come to the so called 'third way' - cutting taxes, but for the best target group of people, the poor. The best benefit you have with this? Poor people are generally more likely to spend money than rich, so if you cut their taxes, you can be confident almost all of it will be spent, thus boosting the economy. Furthermore, you'll have the benefit of increased capacity where the poor are more interested in working longer due to receiving more money for it, although for the very poor who are already working flat out this wouldn't have so much of an effect. Still as mentioned before it's not such a big deal anyway, since in a recession you're interested in getting demand up, rather than increasing the maximum capacity of the economy. Meanwhile forget about trickle down - with this idea you'll have a trickle up effect. The poor people get their taxes cut, meaning they go out and spend money. That means businesses hire more people, meaning those people in turn can afford to go out and spend money, and so on. Obviously you can extend this to pay money to those not earning enough to pay taxes and achieve the same boost to expenditure (in effect having a negative tax on such people). The best thing about this though? It's the poor who benefit. Those who can most use the money get to have some, so they can afford to feed themselves, to clothe themselves, to find shelter. A better alternative IMO than having that money go to line the pockets of the rich who already have all such necessities and a ton of luxuries ontop, and who sometimes start frothing at the mouth at the idea of money being spent to stop children starving on the streets. You also have other benefits - reduced crime, a happier population, improved social cohesion/reduced unrest, etc.