It would also stimulate an incredible amount of inflation by increasing the money supply by about 125,000,000,000. (assuming 250 million americans recieved these cheques). The inflation would be insane. Absolute levels of wealth do not matter because these days money is ‘fiat’ or merely has value because the bank that issued it (like Bank of Canada) says it has value and has a monopoly (counterfeit aside) on printing the stuff.
Inflation would probably be around 100% if the government decided to do this.