[GraniteStateConservative]

No, they'll pay off debt or put it into savings. The poor consume more and save/invest less.

[tnlibertarian]

What happens to that money in savings? It is invested. If it is invested in companies, they have money to buy capital. In addition, a wealth factor exists which states that when a person believes themselves to be better off financially, they will have a higher propensity to spend. By having more money in the savings account or less debt, the person will spend a higher portion of every check they receive. That means that a person who saves that $400 may end up consuming more than that amount. Also, many "rich" are small business owners who will invest that money into their businesses directly by purchasing equipment, or with their cut in the marginal rates, hire another employee.
You're right, the poor will spend all of that rebate, but so will everyone else that doesn't bury it in the backyard.