Yes, I think it is possible to comfortably pay the bills in one's home if one is carrying consumer credit debt, because if the person has a large enough income, they can pay their credit card bills as well as pay their other bills. That is unique though; most people with consumer debt really struggle.
I definitely think that it is more than possible to comfortably pay the bills in one's home even if one is carrying the consumer credit card debt. All it takes is a lot of sacrifice and personal responsibility. Those however are a trait that do not exist much in today's society.
The key is is simply to make enough money. If you have enough money to pay your bills and have consumer credit card debt, just keep paying your bills and put a tiny bit of money away each week. In time, you will be able to pay off your debt. Not very complicated.
Debt payments carry interest, which must be considered "wasted" money. Interest is the price you pay for borrowing money. When paying off debt, you are paying back the bank money that could have been going to anything, including bills and savings. Credit card debt is a drag on anyone's personal budget.