The outlines of the answer, however, already are clear. Officials have said repeatedly that Treasury does not have the legal authority to pay bills based on political, moral or economic considerations. It cannot, for instance, set aside invoices from weapons companies to preserve money for children’s programs.

The implication is that the government will need to pay bills in the order that they come due. President Obama has warned as a result that the government “cannot guarantee” payments of Social Security benefits or other popular programs. Officials also have disputed the assertion of some Republicans that the government could prioritize interest payments.