Wouldn't stimulus by cutting peoples taxes (versus this government stimulus) be clearly more effective? Cutting taxes would achieve the exact same goal, except the stimulus funds would be better directed, and the money wasted by government would be saved?

Wrong. The government is too big to be anything less than precise and efficient with our money.
Think about it...if you need your oil changed, what will get it changed quickly and cost effectively; changing it yourself, or filling out the forms to have a federal agency reserve tax revenue in order to sub-contract out the job of deciding which oil-change companies are local to you so that a local representative can petition to have your oil change officially designated as "necessary" before hiring out the job of scheduling your oil change with a company that currently services the make and model of your car?
You gotta trust in government. They's smart. Plus, republicans are mean and there is SOOO much money wasted in wars and in un-paid rich person taxes. Not to mention that GWB should be brought up on war crimes.