John is right. This usage of "if" to mean "even if" is actually fairly common, but it's only used in sentences with the same structure as the one you quoted: "I couldn't X if I wanted to," "I wouldn't X if you begged me," "I couldn't X if my life depended on it," and so on. For example, "I wouldn't marry you if you were the last woman on earth" means "I would never marry you, under any circumstances, even if you were the only woman alive." The word "if" will NOT have this meaning if it comes at the beginning of a sentence. A sentence with the structure "If X, then Y" will not mean "even if." For contrast:
[A] "If you begged me, I wouldn't leave." = I'm planning to leave, but if you were to beg me to stay, I would stay.
[B] "I wouldn't leave if you begged me." = I am absolutely not leaving, under any circumstances, EVEN if you beg me to leave. (The meaning here could also be simply "if," the same as in sentence [A], but the context and the speaker's tone will usually tell you which meaning is intended.)