I wouldn't believe that. As someone who has worked in the collections world for years, I can say that your house is safe. Even in a bankruptcy they won't take your means of survival away from you. It is true that if you are in enough debt or if you file a chapter 7 bankruptcy that they may force you to sell some of your more valuable and unneccessary assets, but your house is safe. It is just a collection scare that they use.
My recomendation is to read the Fair Debt Collection Practices Act
This is the law that governs what debt collectors can and cannot do. It tells you pretty much exactly what they can and cannot say too. My advice to anybody dealing with any collection agency is to tell them not to contact them by phone and to communicate everything in writing. What they say on the phone is hard to prove, but everything they write can be used against them. Let's see them threaten to take your house away in writing.
What they can do is file a lawsuit against you for the amount of the debt. If they obtain a judgment against you, then the court will require you to pay it. You will be able to work out a payment arangement with the court to do that. They aren't going to just storm your house and start taking things though. This is the beauty of living in America. There are laws they have to follow. A judgement is just like getting a fine for a large traffic violation. People don't always have the $3000 to pay for their DUI, so the courts work out a payment plan.
Don't worry too much, Old Lady. (gosh that feels weird to say lol) There are several steps your credit card company will go through before it goes to judgment. They will try to collect from you first. Then they will try to negotiate with you to pay less. Then they may sell it to a collection agency that will do the same thing. It could actually get bounced around between a couple collection agencies before they finally try to get a judgement against you. Even then, there is a process that has to be gone through. Your house is safe, but you will have to work something out to pay off the debt. Many people are in this same situation right now, so the credit card company has probably already created a process for it.