二の句がつげない

The complete sentence is as follows.
彼女は二の句がつげなかった。そしてさっさと部屋から出て行った。

What is つげ in the sentence? The closest I can get is 告げる, but this is a transitive verb which doesn't go with が. The closest intransitive verb is 次げる, the potential form of 次ぐ. I'm not sure as it doesn't make sense to me in the context.

次げる is close, but it's actually 継げる, i.e., the potential form of 継ぐ. 二の句が継げない is a set expression.