Allen_Reed

USCIS does care if you file your taxes. They are not completely separate issues. USCIS requires that all sponsors (even those that don't qualify on their own) have filed their taxes. If you have not and were required to, then you cannot be a petitioner and your wife cannot immigrate to the US. They don't not care if they were filed late, though. File them now. You will also need to include receipts of filing since you are doing it right now and it will not check out in their system.

Good, get those returns filed. Unfortunately, if you owe taxes the unfiled return penalty is pretty stiff. Once the returns are filed and the exact amount due is known, you should be able to easily get an installment agreement if the total amount owed is in the range you're talking about. I don't think they ordinarily file liens for less than $10,000 unless there are extraordinary circumstances involved. Good luck and hang in there!

Allen,
You really have two issues here: the IRS issue and the immigration issue. As to the IRS issue, if you were on unemployment in 2010 and 2011 I would assume that you are not liable for any additional income taxes. You're only required to file a return if you owe taxes or you want to collect a refund of overpaid taxes. You didn't mention your 2012 return, but assuming that you got an extension your 2012 return will be due on or before October 15, 2013, and your 2012 return should be the tax return that you include with the I-864. So go ahead and get your tax returns filed. Make sure you keep copies of all of your returns, W-2s, and 1099s, because with the government shutdown affecting the IRS as well it may be many weeks before you could obtain a copy of a tax transcript.
As far as the immigration issue goes, USCIS is only looking at your financial status, and is using the tax information to determine your income. USCIS doesn't care and has no jurisdiction over whether you filed your tax returns late, it just wants to see the financial information. If you have a tax due balance with the IRS that is large enough, the IRS could file a Notice of Federal Tax Lien against you, but at most USCIS would deduct the amount on the lien from your annual income for purposes of calculating your financial position.
The bottom line is that you will probably still need a joint sponsor, but based on the information you've given the additional work that you'll need to do to get current on your tax returns should not cause you problems with the IRS (assuming that you do not owe any additional income tax) or USCIS.