Earlier quoted context omitted.
You can use the $900 in capital losses to offset your income (up to $3000). According to the IRS, you would have only $100 in income ($1000 - $900). So in your example, you would have $100 cash and tax liabilities on $100 in income. You will only run into a problem when you exceed $3000 in capital losses, that is when you would have to rollover your losses to the next year.
Still seems like a problem to me.
Tax tip from a non-lawyer/non-accountant - Immediately sell a percentage of your newly mined bitcoin equal to your marginal tax rate. If your tax rate is 25%, sell 25% of your bitcoin as soon as it is mined. Those coins already belong to the US government. If you don't convert to cash immediately, you are basically leveraging the government's money to invest in Bitcoin speculation.