The first outcome would be that the government would have to pay higher interest to borrow, meaning that government debt would cost us more. There is some chance that the higher interest rates would find their way into the private sector, for example home and auto loans or credit card interest rates.
Of course, if you are a person who loans money to the federal government, buying Treasury bills, notes or bonds, you will earn a higher interest rate. That might not hurt your feelings. Like many things, a downgrade will create winners and losers.