I often tell people that they might simply deny every allegation of the petition and put the plaintiff to the burden of proving the case. In some jurisdictions, however, a pleading must be “verified.” That is, you must swear to the accuracy of your pleadings – although I don’t know what the consequences of verifying a pleading that later turns out to be untrue are. Very likely, except in unusual circumstances, there are no consequences if you have any basis for denying at all. It seems likely, although I am not completely certain, that California is a jurisdiction requiring verification. Or to put it slightly differently, in many situations verification is required – I don’t know if there are any in which it is not. Check your rules of civil procedure.
Here is the rule:
Code of Civil Procedure section 437 authorizes denials based upon lack of information or belief "If the defendant has no information or belief upon the subject sufficient to enable him to answer an allegation of the complaint," it is established in this state that denials in this form are limited to situations where the defendant is not able to deny or admit positively. [5a] Accordingly, if the matter is within the defendant's actual knowledge or by its nature is presumed to be within his knowledge, or if the defendant has the means of ascertaining whether or not it is true, a denial on information and belief or for lack of either will be deemed sham and evasive and may be stricken out or disregarded. (Mulcahy v. Buckley, 100 Cal. 484, 486-489 [35 P. 144]; Bartlett Estate Co. v. Fraser, 11 Cal.App. 373, 375 [105 P. 130]; [242 Cal. App. 2d 792] Zenos v. Britten-Cook Land etc. Co., 75 Cal.App. 299, 304 [242 P. 914]; Goldwater v. Oltman, 210 Cal. 408, 424-425 [292 P. 624, 71 A.L.R. 871]; Dietlin v. General American Life Ins. Co., 4 Cal. 2d 336, 349 [49 P.2d 590]; Zany v. Rawhide Gold Min. Co., 15 Cal.App. 373, 375-376 [114 P. 1026]; Taylor v. Newton, 117 Cal. App. 2d 752, 760 [257 P.2d 68]; Oliver v. Swiss Club Tell, 222 Cal. App. 2d 528, 538-539 [35 Cal.Rptr. 324].)  Consistent with this rule, therefore, "if the answer fails otherwise to put in issue the material allegations of the complaint, judgment may be rendered and entered on the pleadings."
In other words, under some circumstances, you can deny on the basis of lack of knowledge or information, that might be disregarded if you are presumed by the law to know the truth of the allegation. Whether a person is presumed by the law to know about old credit card bills is not clear. The best solution might be to deny on the basis of lack of information and belief, and then follow up immediately with a demand for a bill of particulars. If the plaintiff can present you a bill of particulars (unlikely), you might then have to take a second look at the issue.