Yes, at least the IRS has (I believe) released a statement saying that mined cryptocurrencies are to be considered income subject to normal deductions. So, the situation you described where you can end up owing more tax than what you "earned" is not only possible, but likely exactly what the IRS is hoping will happen.

I'm writing this series of posts to, hopefully, reason these exact sorts of questions out and provide a reasonable tax strategy that will hold up to scrutiny under the good faith clause.