If you are a non-citizen, they can also use that refusal as evidence that you are not 'entitled to enter the United States.' In theory that alone is not sufficient to result in denied entry, but in practice it seems that border guards have a great deal of subjective leeway about things.
If you are a US citizen, they cannot deny you entry at the border. However, the device might still be confiscated.
Which isn't to say that it hasn't gotten a lot worse in the US recently.