This isn't true when it is the issuing government (as opposed to a private bank) defaulting. It undermines trust in said government which sort of renders the entire currency meaningless.
It is the opposite.
This stalemate is good for the dollar because it shows that a number of politicians are serious about reining in spending. The USG will stop entitlement spending before it stops bond redemptions at maturity and interest payments. The equity markets are high in recent years only because of money printing. People think that markets crashing because of the stalemate is "bad" whereas it is a pricing in of the necessary economic (painful) medicine which needs to be taken now instead of an (agonizing) Zimbabwe-like currency collapse taken later.
Once in a blue moon you people need to abandon your weird-ass views and think logically.
The ONLY basis for the worth placed in the USD is the faith in the US Government.
A default of the US Government undermines faith in the USG, therefore harming the USD.
The USG owed value to two people: People who own their currency, backed by the full faith and credit of the US Government, and people who own their bonds, also backed by the full faith and credit of the US Government. If they default on their bonds then clearly the full faith and credit of the US Government is useless, rendering the dollar worthless.
According to your twisted logic, a person's credit rating should go UP when they declare bankruptcy since they now have fewer obligations and thus have more capacity to pay you.