They can't compel you to decrypt anything, and powering down is a good idea.

There are consequences for not decrypting, though: for a U.S. citizen, they can seize your stuff for up to 5 days. For non-citizens, they can elect to not let you in.

Concerning "obligated", I would point out that regulations aren't laws. Governing bodies can say whatever they want, but that doesn't make it so. For instance, the TSA continues to publicly insist that ID (especially "Real" ID) is required to fly within the U.S., but it's not.