Yes, wealthy individuals will put the money into stocks, bonds, or bank accounts - not under the mattress. But public companies' market cap rising a bit has a much less direct effect on jobs than creation of demand for local goods and services. Putting extra cash in a bank account is even worse -- a much simpler way of getting banks to lend is to reduce the prime rate, not to increase the savings rate.
Please tell me where this multiplier comes from? If money was multiplied through taxes the USSR would still be around and booming as they had an effective tax rate of 100%. So do tell please.
Try reading a couple months of Paul Krugman -- he explains this particularly well.