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Who is this debt owed to? USDA? What type of mortgage are you trying to qualify for?
Where did they specifically find this debt? When they ran a CAIVRS check? Did you have to call a phone number at USDA to get more information about it because the loan officer didn't have a ton of info on it? If so, that sounds like they found something in CAIVRS.
CAIVRS is run whenever someone qualifies for a government mortgage, if there is delinquent federal debt it needs to be satisfied prior to being able to qualify for a government mortgage. More info on it in the below FAQ:
http://www.hud.gov/offices/hsg/sfh/sys/caivrs/caivrs_faq.cfm
Due to you qualifying for an FHA loan, it sounds like it may have been a CAIVRS hit. Call up your loan officer and ask if it is, and if so, there is a phone number they can provide you where you can call in and ask further questions pertaining to it. It's not that there is a SOL or not, it's that you defaulted on government debt. So you could get a conventional mortgage and probably not have any problems (as long as otherwise you qualify for a conventional mortgage) but since you are qualifying for a new government loan that is very likely the issue. Worst case, you may have to pay the claim in full in order to proceed with government mortgage financing.
Unless you have 20% down you are correct, that FICO score won't qualify you for conventional. With 20% down that FICO score should be fine though. A 660 score you should be able to just need to put 10% down with conventional. Hopefully USDA is willing to waive the claim.