Throughout the United States, you have an almost unlimited right to be free from searches by law enforcement absent probable cause that can be demonstrated in court.
Except:
* This doesn't apply at the border.
* Regardless of whether the police have a right to search you, anything you do to obstruct a police search can be used as the basis of an orthogonal criminal charge.
Similarly, throughout the United States, you have an almost unrestricted right not to answer questions from law enforcement.
I ask:
* Accepting that the outcome of not cooperating cannot be denial of reentry, to what extent does this principle apply at the border? The right to be free of unreasonable search is at the core of the bill of rights, and the word "reasonable" seems to mean "all bets are off at the border".
* Regardless of whether police have a right to question you, things you do to obstruct them may be the basis of orthogonal criminal charges. For instance, Terry stops, Hiibel, &c.
Generally, as an avid civil liberties enthusiast with zero legal qualifications, my perception is that your rights are at their practical zenith in a courtroom, and at their nadir in a confrontation with on-duty law enforcement.