Even if you file an extension you are supposed to make an estimated tax payment based on what you think you owe. It only extends when you have to file.
If you are eligible for USDA and are a first time homebuyer then contact your local USDA office. They have a policy on the books that basically states that if the loan will benefit the government because you owe a government debt then it is basically used as a compensating factor in doing the loan if somehow the government will be paid off. If you are a first time homebuyer and qualify for the tax credit then you could use that as a point in why they should do the loan. The IRS would receive the payment in full this year if the USDA did this loan for you 
Unfortunately I dont live in a rural area.
That is what I plan to do also once I am able to move forward with loan application. It only makes sense for the government not to use it to deny the loan but to make it a reason (along with all the other positives on the loan) to proceed with the loan.
Check with HUD and see what their policy is. They may also have the same reasoning on FHA loans. It is not like you have taxes due from 10 years ago. It is not uncommon for people to end up owing taxes and working out a payment plan.
