My understanding is that the Supreme Court has decided that refusal to allow a search does not by itself constitute "reasonable suspicion," and that a search performed for this reason will be deemed unreasonable and any evidence thus obtained would not be permissible in court.
The overstepping officer is counting on the citizenry not knowing what their rights are or being in too much of a hurry to demand to have his civil rights respected. By simply saying, “I don’t object if you obtain a search warrant and I’m willing to wait” throws a new spin on the situation.