Governments issue bonds
A sitting government can issue municipal or national bonds at an interest rate it sets, raising money from the open market — funded only by willing buyers, never auto-purchased by banks.
Governments have a real borrowing tool. From a treasury's Treasury tab, a government can issue a bond — municipal for a city government, national for a national one.
You set the rate. You choose a face amount and your own coupon interest rate. The bond is posted to the open bond market, where players and banks fund it in $100 coupons; the proceeds land in the treasury, and the coupons are serviced automatically each day from that treasury.
No backstop. Unlike the automatic bonds that cover a treasury shortfall, a government-issued bond is never bought by banks to fill it up — it relies entirely on willing buyers. Price it attractively and it gets funded; price it too low and it expires unfunded after a few days. Whatever sold by then becomes the bond's debt.
A real limit. Issuance is capped at the treasury's debt ceiling (about three times its recent revenue), shown as your borrowing headroom. Miss payments and the bond defaults, which hurts future borrowing — so borrow within your means.