That will depend on your jurisdiction. You will need to check with an attorney to be sure of the answer, but it looks like California Code of Civil Procedure 2024.020 governs, and states a party is entitled to complete discovery 30 days before discovery. That would mean you could send a response that you refuse to respond under this rule. However, the Cal. Code also allows a party to complete discovery closer to the trial date under 2024.050 upon motion and hearing.
You may want to discuss this with an attorney licensed in California, who can then draft the proper response. The other side might try and force the matter to a hearing, and having that attorney available to represent you would help as well.
This procedure is proper and has absolutely nothing to do with discovery under Code of Civil Procedure section 2024.020. What you received is a Notice to Appear at Trial and Request To Produce Documents At Trial, which is a substitute for a subpoena to appear at trial. See Code of Civil Procedure sections 1987 (b) and (c).
You are entitled to make objections within five days of service, but the objections are different than objections to discovery. For example, a very common objection if the Notice to Appear requests the production of documents is that the request to produce documents fails to “state the exact materials or things desired” as required under California Code of Civil Procedure § 1987(c). An exact definition does not mean a reasonable description of a category of documents as may be used during discovery.