「」。
She almost slipped up and said "I don't know."
Literal
She [topic-は] narrowly "don't-know" [quotative-と] say-end-up [was-about-to-ところだった].
The 危うく + ~ところだった frame applied beautifully to a verbal near-miss: she nearly let slip something incriminating. 言ってしまう layers ~てしまう ('end up doing, do regrettably') onto 言う — capturing the unintended, blurted-out quality of the slip. The と is the quotative, marking 「知らない」 ('I don't know') as the would-be utterance. Japanese punctuates direct quotes with 「 」 corner brackets rather than English's quotation marks. The whole sentence reads as a tiny moment of self-restraint in conversation.