If one has to borrow to payback does this mean an entity is insolvent ?

Mathematically does the following statement "If we do not raise the debt ceiling we will default on our debt" imply that an entity is insolvent ? For example, let's say I owe a total of $100,000 on my credit cards and $3000 a month. Then tell my creditor if you do not lend me more money I cannot pay you back. Under what scenario is the borrow not considered insolvent ?