You say that you have been served with a summons, demanding payment "or they will sue" you. This is not quite correct. They have sued you, and if you fail to file an answer within the required period, they will obtain a default judgment against you. If they obtain a judgment they will be able to take your "non exempt" property and sell it until the judgment has been satisfied (paid).
The court will not "force you" to pay the judgment, it will allow the judgment creditor to execute (sieze your property). You have certain exemption rights. These exemptions normally (depending on what state you are in) include your "homestead" (your home, sometimes to a certain value), a certain portion of your salary, and other catergories of property. If the property they consider executing upon is exempt they cannot touch it.
Yes, bankruptcy protection extends to credit card debt. In a Chapter 7 bankruptcy, if your assets can all be included in exempt categories, you are "discharged" from your dischargeable debts (usually including credit cards). This means that the creditor cannot take measures to collect these debts (including suing you). In the mean time, when you file bankruptcy the creditors are stayed from attempting to collect these debts, while the bankruptcy is pending. Holders of secured debts are entitled to their collateral and can take that collateral if they obtain "relief from the automatic stay provision.
Another form of bankruptcy is "chapter 13", in which you agree to pay a portion of your unsecured debt over a period of time.