If it's a dead man's switch and you're not a career criminal, I'm sure you could convince a judge that it slipped your mind because of the distress caused by being whisked off to jail. Probably not a guarantee that a judge won't say 'too bad' though.
Then it depends on what you destroyed. If the data is provenly destroyed there are limits to what you can be charged with. If what your hiding is worse this still maybe a viable option. If however the data is still recoverable with your cooperation I believe you could be jailed in contempt indefinitely (until you cooperate).
The longest contempt detention I'm aware of was a very bizarre case involving a guy named Richard Fine who was jailed for something less than 18 months. It was a civil case, and as far as I know he never argued that the information he was being ordered to produce would incriminate him in a criminal matter. His attempts to secure his release involved some conspiracy-theory-level ranting that probably contributed greatly to higher courts ignoring him.
A local judge ultimately decided Fine was irrational and keeping him in jail didn't accomplish anything but taking up of jail space and resources.
In a criminal matter involving even a hint of self-incrimination, I'm disinclined to think a contempt sentence would be allowed to continue indefinitely by US courts absent an immunity deal.
