If you are a US citizen, they are not entitled to your unlocked phone. They need a judicial warrant if they want you to unlock your phone with a PIN/password. It is settled case law that that falls under your protections under the 14th Amendment.

They can take it for a "reasonable amount of time" (inconvenience you for a few hours and make you miss your connecting flight) while they copy an encrypted image. They then must return it to you.