At which point, the judges would simply issue a court order that funded the judicial branch, something they've been doing for years that is blatantly unconstitutional.
The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish. The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behavior, and shall, at stated Times, receive for their Services a Compensation which shall not be diminished during their Continuance in Office.
Read the Constitution before calling something Un-Constitutional. Congress is mandated to pay the Judges and maintain the courts under the constitution.