The Fed will keep printing dollar to keep their balance sheet under controlled. The debt ceiling will be raised again and again. At least they can make the creditors believe they can pay back when due.
Maybe for now, but at some point creditors realize they are not going to get their money. Living above ones means isn't sustainable.
Governments actually can, in theory continue to issue debt in perpetuity as long as their GDP grows faster then the amount of total debt. If GDP grows faster then the total debt as a percentage of total national income will decrease, thus making it easier to service.