If this is your own IRA (not inherited) and this is not your first RMD year, then, yes, you blew the date. Use form 5329 to request a waiver. You aren’t the first person this has happened to, so next year, leave a few extra days. Remember that since your January 2, 2024 withdrawal will be reported as taxable income on your 2024 return but you are using it to satisfy the 2023 RMD requirement, you must withdraw additional funds in 2024 to satisfy your 2024 RMD requirement.
Also, remember that an RMD is not a specific transaction, it is simply the minimum amount you must withdraw at anytime during the year. You can always withdraw more if you want. For example, if your 2023 RMD was $5000, you could have satisfied that by making a $5000 withdrawal at the end of December. But the requirement would also have been satisfied if you had been withdrawing $500 per month for general spending, because your total withdrawals would be more than $5000, and no additional special withdrawal would be needed.
