I'm just guessing here, but the most problematic word on the 4th amendment to attack from the government's perspective is "unreasonable". It's easy to see how a phone border search could be construed as reasonable, and (without digging into this deeply) I suspect that's where most of the push back on this will be.

I suspect the 5th amendment is probably more valuable to the defense here as the password is effectively testimonial and the give us your password or we'll ... is compelled speech.

Either way, it's gonna be many 10s of thousands of dollars in lawyers fees to fight this. Which sucks.