Generally speaking, no, you're not personally responsible for your deceased husband's income taxes. It's possible that if you inherited any property from him the IRS might be able to reach that property to collect any unpaid taxes, but they generally could not go after you personally or after property that you own that you didn't inherit from your late husband.
To get greater certainty, however, and a better answer, I would strongly advise you to consult with a competent local tax professional, such as an accountant or CPA (right now I don't think you'll need a tax attorney, although that could change depending on the precise facts); that person should be able to make the appropriate inquiries with the IRS to find out what's going on with your personal tax accounts - i.e., whether the IRS is trying to assert taxes against you personally - and with your late husband's tax accounts, although in that case you will probably have to have the executor/administrator of his estate (if that wasn't you) sign a power of attorney so your tax professional can speak to the IRS about your late husband's tax matters.
My answer does not constitute legal advice and may not be relied upon by anyone for any purpose and does not constitute an attorney/client relationship or an offer to form such a relationship. This disclaimer is intended to be fully compliant with the requirements of Treasury Department Circular 230 and the terms thereof are fully incorporated by reference. If you wish to consult with me please contact me at dwatchley@newyorktaxcounsel or visit my website at www.newyorktaxcounsel.com