[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.

[GraniteStateConservative]

We're talking short-term stimulus. Investment is long-term. We sent out $600 checks Summer 2001 and just over 20% spent the checks, but the checks only went to people who paid enough taxes (otherwise they got less than that or nothing at all). People who get welfare checks don't save or invest those checks. They spend all of them. There wasn't a jolt in spending because the checks weren't sent to people who would head out to Wal-Mart and boost their sales. The money in 2001 went to people who would stimulate the economy longterm.