Apparently, the answer is "no".  Or, "maybe not". Or "it depends on the circumstances".

I've always wanted to make my interactions with Border Patrol agents at security checkpoints go as quickly and stress-free as possible, for me as well as for the agent.  In the video posted below, watch as several people record themselves 1.) refusing to answers questions about citizenship, 2.) declining to allow their vehicle to be searched and, most amazingly, 3.) being told that they can go ahead without any further hassle!!

A couple of things to notice in this video:

They decline to answer all questions, even ones like, "Are you doing anything illegal?".

The Border Patrol agents seem to avoid giving a direction as an order, instead preferring to use phrases such as "Can you do me a favor and pull over" and "I need you to pull your car over".

Also, notice how many times the provocateurs ask if they're being detained. And how reluctant the BP agents are to say "Yes, you are being detained."  This is because in order to detain you, they (along with other law enforcement officials) have to have something called "probable cause" to do so. And, no, probable cause can not be defined as "you refused to let me search you therefore I have probable cause to believe you're doing something illegal."

See if you're as amazed as I was to see how toothless the Border Patrol is when it comes to being challenged on the legality of their searches.