Debt can infinitely increase as long as it comes with increased productivity. The US debt is serviced through new debt since the gov is in a budget deficit. So far it came with increased productivity so there were no problems. What happens when productivity doesn't increase though? You get Japan, Italy, and increasingly the UK, at major economies.The thing is how is the US govt ever going to pay back the debt of 31.4 trillions, that's close to USD 89k per every soul in the US.
Obviously the US govt never intends to, which is not sustainable. One day the chickens will come home to roost and that day is approaching fast.
This debt ceiling thing is an issue because it is a legal limit only the congress can increase. It becoming material for petty politics shows how dysfunctional and self-harming US domestic politics are. The US govt can't borrow without the congress increasing that limit so it can't service existing bonds. If the US defaults on even a tiny percentage of its debt, it would be really harmful to the USA. US bond interest rates would increase permanently to account for the increased risks with the US bonds, which would in long term cost trillions of USDs to the USA. In short term its effects would be more drastic. The US economy would contract this year.
All of this would happen because of Republicans vetoing the lifting of debt ceiling, effectively banning the US Govt from servicing its debts.