Can the U.S. Constitution borrow money?

Yes. The Constitution of the United States says, in Article 1, Section 8, the second of the "enumerated powers" of the Congress:

Section. 8. The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States; To borrow Money on the credit of the United States;