The United States Internal Revenue Service manual lays out the basic ground rules for "continuity planning", which ensures that the IRS will still be able to function under any number of extreme circumstances. This includes wars, natural disasters, terrorist attacks, pandemic influenza, and yes, even nuclear explosions. (You can read all about it in the IRS manual
In fact, the U.S. Treasury Department has had plans since the 1960s to revive and maintain the American economy after a nuclear attack. After such an attack, economists in secret locations will oversee the apportioning of tax-free cash grants to survivors (a stimulus package), while the government buys up assets destroyed in the attack (like the Troubled Asset Relief Program), and pays off any outstanding bank loans and mortgages. After that, the pre-existing tax policy will likely be abandoned, and the IRS will have to form a new policy for generating government revenue to fund the rebuilding process. No firm tax plan for such a scenario has been agreed upon, but several proposals and guidelines have been prepared and stored at relocation sites for just such an occasion. Which of the plans they opt for will be decided based on the situation on the ground, though one likely system would enact a sales tax as high as 30%.
While nuclear winter won't be enough of a crisis to free us from the IRS, we can take comfort in the fact that the United States Postal Service will also be functioning in that time of crisis. The USPS has an emergency planning manual for just such an occasion. Their post nuclear attack plan has been in place since 1981. Not only will they continue to deliver the mail, they will also have to distribute the 60 million change-of-address forms that they already have prepared and distributed throughout 30,000 post offices. Check out this Brookings article
to learn more about the U.S. government's post-doomsday plans.