How serious is it that I forgot to verify my response to complaint? The plaintiff is demurring my answers.

Lawyers regularly claim it was secretarial or administrative error. Granting a default at this stage would appear to be an abuse of judicial discretion. If the opposing counsel didn't call you before filing the motion, make sure to mention that in your responsive pleadings to the motion. Don't miss the deadline in replying to the motion. Make sure you both filed your versification with the court AND sent a copy of the verification with a proof of service to opposing counsel.

Your answer was not verified? Was the complaint verified? If the complaint was not verified, your answer does not need to be either. His demurrer may be granted, but likely with leave to amend. In which case you can verify the answer and be done with it. In fact, you can probably just do that immediately and serve him. In opposing the demurrer, identify when you served it and attach a copy. And you should really get an attorney. You are very unfamiliar with the procedures being used and that can really lead to trouble otherwise easily avoided.

Demurrers to answers are rare, and most judges find them to be a waste of time. But it is within a party's right to demur to an answer. If the only issue is that your answer was not verified (and the complaint was verified) then the solution may be to just file an amended, verified answer. What might be best for you is not something that can be stated on this forum without at least seeing the complaint, your answer and the demurrer. Take everything to a local attorney for review. You should at least consult with an attorney to see if there may be some other way to respond.