To eliminate the tax, you would have had to sell the stock in the calendar year of your exercise. A "tax abatement" under the Emergency Economic Stabilization Act of 2008 wiped out any AMT liability from ISO exercises before 2008 that were owed but never paid, along with any interest and penalties associated with ISO-related AMT liability. However, that provision no longer applies. There is an AMT credit that you can use (see the related FAQ), but it take years to fully recover AMT paid because of an ISO exercise.
In general, people who are financially distressed by a large tax bill can contact the IRS about paying through installments (use IRS Form 9465, "Installment Agreement Request"). This form lets you ask to pay the tax over a period without penalty.
Offer In Compromise
In limited circumstances, you can make an "offer in compromise" (OIC) with the IRS if you never will be able to pay your tax debts (see the related IRS information page). If accepted, an OIC settles a tax claim for less than its full amount. Though you must pay a fee of $150 to make an offer in compromise, the fee is sometimes waived or refunded (e.g. if the OIC is accepted). When submitting a lump-sum OIC you must make a down payment of 20% to the IRS.
The IRS does not even consider an OIC until it has exhausted other alternatives, such as an installment plan. Economic hardship can cause the IRS to rule in your favor, but the definition of "hardship" is open to interpretation. As one case in 2005 showed (Speltz, 124 TC, No. 9, affirmed by the 8th Circuit Court of Appeals), the IRS can demand payment of the full tax as long as a taxpayer's assets and future earning capacity are sufficient to eventually meet the obligation. In this case, the IRS rejected the arguments (1) that the married taxpayers' standard of living would suffer from paying the tax and (2) that the AMT was significantly more than the stock's worth.
According to experts, the acceptance of an OIC by the IRS typically involves exceptional circumstances, such as long-term illness or hospitalization, or the very severe financial crisis that a retiree would face if forced to deplete a retirement fund to pay a tax bill. You can consult state and local tax professional groups and directories to find CPAs and attorneys who can advise you and help you prepare an OIC if you qualify.