There are several synonyms for the phrase "any day now" including "at any moment", "soon", "imminently", "in the near future", "shortly", "incipiently", "around the corner", "nearing", "about to", and "on the verge". These phrases all convey a sense of anticipation that something is about to happen, without specifying a specific date or time. They are often used in conversations where there is an expectation that an event will happen soon or a situation will change, such as waiting for a job offer or the birth of a baby. Regardless of which synonym is used, the implication is that the wait will soon be over.