Tax debt is a vicious cycle sometimes...I know because I've been there. In my divorce, my ex assumed sole responsibility for a tax debt for which a Tax Lien had been filed. Since he was on an installment agreement and planning to continue renting for several years, there was no incentive for him to pay off the lien, even though he could have. What I found today is that you can request a Withdrawal of Notice of Federal Tax Lien if you write a narrative explaining how it is in the best interest of the government and the taxpayer, or how it expedites the collection of taxes. I argued both cases - in my situation, the tax lien is affecting my ability to obtain a mortgage at reasonable interest rates, causing me to need extra cash to pay points to buy down the interest rate. I offered to pay the remaining balance in exchange for the Withdrawal (which would essentially make it like it never happened - better than a Released status). My point to the IRS was that I could either pay the mortgage company or I can pay them if they withdrew the lien.
In your situation, compare the difference in the monthly mortgage you obtain with and without the lien. You could argue that you could pay more per month on an installment agreement if you knew you could obtain a reasonable interest rate for a mortgage, which expedites the collection of the tax debt. Maybe suggest 1/2 the difference between the lmortgage-with-lien interest monthly interest amount vs. non-lien interest rate? Really don't know what to suggest though - shooting from the hip.
Look up form # 12277 on the irs web site.You will also need to access the Technical Services form which will be referenced on that form. I called the number listed and the gentleman I spoke with was very helpful. He also stated that the turn-around time is usually within a week for a decision.
Good luck to you. Hope this helps.