You may be able to sue them later but I guarantee they are not taking no for an answer.
And, the important thing is that anything they find would be fruit of the poisonous tree and would thus be inadmissible in any criminal prosecution of the person refusing the search.
Correct, unless it was in the search warrant. If the warrant said they were looking for the person involved in the bombing and that was it, you could have 20 pot plants growing and there would be nothing they could do.