That is one way to "inject" money into the system. The other way is to give people tax breaks. No doubt about that. But again you want to give the break to people who will actually spend it. Give a millionaire a tax break and he/she will probably either invest it in a bank in China or buy some stock of a relatively successful business or even park the money in a Swiss account. The money will disappear from the primary market and get sucked into the secondary markets. And money in the secondary market will do no good whatsoever to help the economy. The economy is in the primary market. So to ensure that the money stays in the primary market the tax relief has to go to people who will actually spend it. Again, key word: spend.
Lastly tax relief only affects people who still have a job and are paying income taxes. For the people who have lost their jobs, such relief means precious little. No income, no income tax. No income tax, no tax relief. Tax relief will provide relief to those already employed but will not revive the system if a large number of people remain unemployed. The strategy therefore should rest both on re-employment and relief. Not either or.