The U.S. State Department can deny a passport for a host of reasons. However, you can't be denied a passport for owing back taxes, except under certain circumstances.
Taxes and Passports
You cannot be denied a passport for owing back taxes under ordinary circumstances. The exceptions are covered under 22 CFR 51.70 (Denial of Passports regulation). You fall under the Denial of Passports regulation if any of the following apply: the Internal Revenue Service has started court or grand jury proceedings against you and you are subject to a subpoena; the IRS has filed criminal felony charges against you; you are out on bond or there is a warrant for your arrest; or if a subpoena was issued by the IRS for a federal civil prosecution.
If you are denied a passport for owing taxes, you must pay the back taxes in order to lift the denial. IRS must drop its case against you, and notify the State Department in writing that the passport denial is no longer in place.
Federal and state law enforcement agencies can request that you be denied a passport if you have a federal arrest warrant, a state or federal criminal court order, or if a condition of your probation or parole forbids you from leaving the country. Merely owing back taxes is not a federal or state crime.
Other Reasons for Passport Denial
Warrants are issued by courts, at the request of government agencies, to compel a person to appear. If you have a warrant in the U.S. Marshall's Warrant Information Service database, there is an outstanding request for your extradition, or you owe $2,500 or more in back child support, you will be denied a passport.
If you have a valid passport, and your application for a new one would be denied, you can continue to use the old passport unless a government agency requests, and is granted, its revocation.