You can't recharacterize contributions whenever you want - you have until your tax filing deadline (with any extensions) to do so. I don't know if there is an exception for "I made a mistake and the IRS caught it after my deadline" - I would suspect not, but maybe. Something to ask about.
I'm thinking the IRS saw that you had an unsupported IRA deduction there and just disallowed the whole thing. I'd probably contact a CPA who is well versed in dealing with the IRS as this isn't a simple "whoops we messed up - we're paying the amount shown on the bill" situation. More of a "we messed up, but you're asking for more than we actually owe" situation, which as DavidAnnArbor's link will show you will be more difficult. Anything other than just paying the bill is a big-time pain in the ass to deal with.
Did you use a tax preparer? If so, get in touch with them - they may cover the penalties and interest if it was their mistake. H&R Block did this for my now wife when they had signed her up for a tax-credit she most definitely did not deserve. If I recall, she paid the full bill and H&R Block reimbursed the penalties and interest. The letter from the IRS was the first piece of mail she received after moving into my condo. If you used software, who's? Turbotax has always made it very obvious to me that the recharacterization must come from both accounts when we've done it in the past, but others might not be so clear, or might have had a bug and you can be reimbursed similarly.