The most important aspect of the claim about spending money is the broken window fallacy. Henry Hazlitt wrote a great book on the subject called Economics in One lesson.
The simple example is that we can't go around breaking windows to stimulate the economy. Sure, the window manufacturer and the window replacement companies might benefit, however that money which went towards the window could have gone elsewhere.
Engineering taught me one very important lesson. We can never get something for nothing. There is always a trade off. If the government is handing out money, it has to come from somewhere. Its either taxes, which means that tax money collected can't be spent elsewhere. Or it has to be printed, which is inflation.
Some people say, people aren't spending it, they are saving it! Thats important too. Unless they are keeping it in their mattress, that money is deposited in banks, which loan out the money for capital improvements, etc.
Lastly, my anecdotal experience is that "free money" tends to be squandered more than earned money. Which means poorly allocated funds towards resources less valuable to a strong economy.