The latter is not asserting any rights since you cannot permit them with 'you may search me' while simultaneously claim you are not consenting. 'You may search me' is consent.
The former exchange may be followed by:
1. The officer reaching for your vehicle, you instinctively reacting to block him, and we have our aggression.
2. The officer asking why not, telling you he is now going to have to throw the book at you and every minor violation that everyone does will now come up (the easiest? Speeding violation for 5 over).
3. The officer coaxes you. You stand your ground in the same manner. You are being bullheaded. Try to convince your fellow man after an encounter like this. Almost certainly you'll be told that you should 'pick your battles'. This will certainly be followed by #2.
It is letting folks know you may be asserting it after the fact and you aren't waiving your right. What you are doing is establishing that the search isn't voluntary and that your cooperation is not consent.
I don't know how different circuits would look at it. My understanding is that this would not be effective in the 5th and 11th circuits since they hold that you consent to searches when you get in line and you can't revoke that consent. But other circuits haven't gone that far. That means that if they want to hold the search as lawful, they have to establish that it is a valid administrative search, and that consent is not required.
It would be clearer if "you may" was replaced by "I am aware you may" clarifying that this is not permission but a statement of possibilities.
The former exchange may be followed by:
1. The officer reaching for your vehicle, you instinctively reacting to block him, and we have our aggression.
2. The officer asking why not, telling you he is now going to have to throw the book at you and every minor violation that everyone does will now come up (the easiest? Speeding violation for 5 over).
3. The officer coaxes you. You stand your ground in the same manner. You are being bullheaded. Try to convince your fellow man after an encounter like this. Almost certainly you'll be told that you should 'pick your battles'. This will certainly be followed by #2.