From the piece:
In theory, Treasury might be able to prioritize bond payments above all else, says Steve Bell of the Bipartisan Policy Center. The computer system that handles U.S. sovereign debt,Fedwire, is separate from the system overseeing payments to government agencies and other vendors. Yet it’s unclear whether Treasury has the legal authority to prioritize in this way — the agency has never dealt with this situation before. “Anyone who says they know for sure whether this is legal is not telling the truth,” says Bell.
Back in 2011, Toomey proposed a bill that would authorize Treasury to pay bondholders before anyone else. Assuming his bill ever passed, that would resolve the legal issues. But the government would still have to decide what to do about all its domestic obligations. And that could get messy.