My question assumes—perhaps incorrectly?—that every dollar the Federal
government owes must be paid back on some schedule.
You assume incorrectly.
By definition, if there is no deficit and no surplus, then the Treasury makes interest only payments on a net basis, and issues one new dollar of federal debt for each dollar repaid. The maturities of particular bond series that are issued by the Treasury are irrelevant as a result. Also, a large share of the national debt is maintained only in government accounting ledgers and has no maturity date (e.g. the "Social Security Trust Fund").
To be clear, "deficit" is an income statement concept and "national debt" is a balance sheet concept. "Borrowing" can be used in either sense and I have read the OP in the only sense that it can possible be consistent and form a well posed question.
A deficit means "net borrowing", i.e. spending more than incoming government revenue. One would need massive surpluses and not merely the absence of a deficit not to issue new national debt instruments all together, and the mix of maturities varies significantly from month to month as a matter of Treasury Secretary discretion.
Individual national debt instruments like treasury bonds, savings bonds, and treasury bills are paid off from time to time, but the Treasury simply issues new ones at auction many times a year to borrow funds to make up for those that were paid off. One of the more technical, but important, tasks of the Secretary of Treasury through his or her deputies, is to decide what maturities of particular national debt instruments to issue at any given time.
The exact mechanics of the Treasury bond markets is beyond the scope of Politics.SE but it is it outlined in general here. Basically, the Treasury Department has standing orders to continually refinance the national debt.
So if Congress stopped borrowing, presumably the debt would be paid
off after a certain amount of time. How long would that take?
No. It would never be paid back. The national debt would stay the same forever.
If you are paying off the national deficit from sources other than cash reserves, then you have, by definition, a surplus.