Household debt slowly adds up making the overall economy worse and worse. It starts to create a spiral effect where customers can no longer afford to buy items they used to causing businesses' not to get the money they used to causing them to go out which spirals up the government creating a huge debt for the country.
Households cannot avoid most taxes (e.G service charge from restaurants). When households are in debt, that does not mean they do not go out to restaurants to eat or they do not pay road tax annually. Even if they are still in debt, they will still need to pay these unavoidable taxes to the government. Secondly, households will continue to purchase products even if they are in debt (may even purchase products through debt). It may even increase a country's GDP because households spend more through debt.