This is confusing; what happens to you if you refuse a warantless search of your property?

I'm a US citizen returning home. Do they just... send me back out of the country? :) I don't suppose they'd have the grounds to arrest me since there is no law that I can see being broken. I suppose they could keep the device until such time that a warrant could be obtained to digitally search / break into the device (but that requires some reasonable suspicion - simply refusing a warantless search isn't it).