If you meet the income requirements, you should be fine. I am a bit confused whether you are an LPR applying for citizenship or whether you are concerned about applying for a relative. Please clarify.
It should not be an issue. Obviously getting your problems resolved with the IRS would be a prudent move. They are only after one thing, money. You should call them and work things out with them. They usually do not issue tax liens unless they can't get a hold of your refunds. An offer in compromise would be a better way to get onto a monthly payment plan. Anyhow, the question as to whether you owe local, state or federal income taxes is usually not asked during the green card/adjustment interview but during the naturalization interview only. As long as you can show the minimum income based on your Adjusted Gross Income on your federal 1040 tax return which meet the minimum poverty guidelines for 2014 promulgated by the HHS you should be fine. Again, during a naturalization interview the officer would not even approve your case if you cannot show a payment plan agreement since you are trying to prove GMC-Good Moral Character but not in a green card interview. Here the focus is more on the viability of the marriage I.e. the bona fides of the marriage. Good luck.
As a general rule, the application would not be "out right denied" but a request for evidence would be issued, giving you an opportunity to add a joint sponsor if there is anything that is insufficient about your financial sponsorship.