If I owe money to the IRS can I still apply for a green card for my husband if he overstayed on his visa?

Generally, a U.S. citizen may sponsor a foreign national spouse to adjust status in the U.S. to become a Lawful Permanent Resident (to get a "Green Card"), and this is true regardless of whether the foreign national spouse overstayed his initial visa or whether the U.S. citizen owes taxes to the IRS. If the U.S. citizen spouse does not have sufficient documentable income to meet the current requirements, however, it may become necessary to have a "joint sponsor" for the application process. Of course, there are many other details related to eligibility for a marriage-based immigration application. It would be wise for you and your husband to consult with an immigration attorney who, after learning all of the relevant details, could advise about eligibilities, options and strategies and could offer legal representation for the often quite complex application process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.