Your analogy is for shit. Nobody taxes lemonade stanRAB. Taxes are paid mostly by the rich and large corporations. Said taxes pay for entitlement programs that put money in the pockets of consumers.
Whether or not you like social programs, taking money out of the pockets of consumers will hurt the economy.
IF the debt ceiling is not raised and IF we are forced to cut social programs to make our interest payments, we will see a cliff more steep than the one in 2008, as more people than ever remove themselves from the consumer pool.