A Demurrer based on the Statute of Frauds will only be successful if the plaintiff alleged an oral agreement, not a written contract. A Demurrer is based on the pleading on its face. This means that if the Complaint says a written agreement exists, whether or not it does, the Complaint will likely be upheld. If the plaintiff did not allege a written agreement, then the Statute of Frauds argument may be successful.
Even if the Complaint alleges a written contract, you can bring a Motion For Summary Judgment later in your case after some discovery. You can also request attorney's fees, especially plaintiff pled that a written contract exists and then failed to provide it to you during discovery.
If you choose to proceed with a Demurrer, you will want to show that plaintiff failed to state a valid cause of action and/or plaintiff's allegations are uncertain.
The above answer is not "legal advice" as specified under any pertinent rules governing the Professional Responsibilities of Lawyers and should not be relied upon. An attorney-client relationship has not been established by virtue of this correspondence. Legal issues are often complex and involve local laws and facts which may not be effectively communicated without a complete consultation.
It is not required that there be attached to the Complaint copies of the written documents upon which the plaintiff's claim may be based. It is probably sufficient that the Complaint alleges the existence of a such written document or agreement in which you gave such a guaranty. If the Complaint contains such an allegation, your demurrer would not be well taken and you might as well save the effort.
I agree with my colleague that your better bet is a motion for summary judgment if you think they can't prove their case about your personal guarantee. Demurrers rarely win cases. They generally do no more than waste time/effort/money, and since you're pro and the credit card company as a corporation has a lawyer, only they have an upside here. Also, they educate your opponent, and frankly, if it's a lawyer against you in pro per, chances are they know what they're doing and you don't.
Answer the complaint, do discovery to get every document and argument they're relying on to support their personal guarantee claim, and then move for summary judgment.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
"Documentation or proof" is not required to be provided at the pleading stage.
You obtain such proof by propounding written discovery and taking depositions.
If the amount of the alleged debt is substantial, I would strongly urge you to retain an attorney.
A layperson such as yourself, no matter how astute, will be no match in court for an experienced attornney.
Feel free to contact me by telephone or e-mail if you would like to discuss this matter.
PLEASE NOTE THAT THIS RESPONSE SHOULD NOT BE CONSTRUED AS A LEGAL OPINION OR ADVISE, AND DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP. IN ORDER TO RENDER A LEGAL OPINION OR ADVISE, THE RESPONDING ATTORNEY WOULD NEED FAR MORE INFORMATION THAN HAS BEEN PROVIDED, AND WOULD NEED TO BE RETAINED PURSUANT TO A WRITTEN FEE AGREEMENT.