Generally speaking, the underwriter would have no way of knowing that you owe back taxes unless (1) they ask for a copy of your current return (that shows a balance) OR 2) a tax lien has been filed.
If you didn't file for 2009 because you fell under the income filing threshold and you do not have any outstanding tax liability except for 2011, it might be beneficial to file an extension for your 2011 return. If you file an extension, you may be liable for filing penalty if you fail to make a good faith estimated payment with the request for extension (IRS FORM 2848).
If you cannot pay the amount due within 120 days, the IRS offers a a short-term extension if you can pay in full within 120 days (no fee assessed but interest and penalties will continue to accrue). If this is a feasible option, you can call the IRS at 1-800829-1040 to arrange such.
If this is not an option, then the outstanding liability and your options for installment depend on whether you owe 1) $10,000 or less; OR 2) Over $25,000.
You can get answers more specific for your situation at :