Most budget experts see a move to raise the ceiling as inevitable. That has always occurred in the past, although sometimes with delays from political brinkmanship that push the Treasury to the edge of its ability to stay under the limit.
This time, many Republicans in Congress see withholding approval of a debt-cap hike as a tactical weapon to win new curbs on federal spending.
An outright refusal to raise the ceiling could have serious consequences in financial markets and the economy. It would raise the risk of an upward spike in interest rates, as bond investors would come to have less confidence in America's creditworthiness.
When and if the Treasury would have to default on public debts is a more complicated question. Some deficit hawks say fears of a default are overblown. They argue that after a refusal to raise the ceiling, amid deep cuts in federal spending, the Treasury could continue to pay interest and principal on its debts.
As it now stands, once the ceiling is reached the Treasury would be in a severe bind. It would have a legal mandate to spend money on a range of federal programs (from salaries to tax refunds), a mandate not to borrow any more, and thus not enough money to go around.