Still waiting for that direct quote, either that are you have told a lie.
When you are in the process of negotiations it would be very stupid to say” I favor a government shutdown”. A shutdown means the process has failed, you are going to take the heat for no honest effort to negotiate.
She was being positive and providing cover for the opposition in the event Boehner can bring them around. It is a gesture to say “you can go ahead with this and merely look like you agreed with our proposal because you don’t want a shutdown either”. They can then claim they did it for the good of the country.
There is a lot going on in the way this is handled by the GOP in regards to public perception.
No matter what, anything that happens will have to get through two democrat gates to become law. Obama could just veto the whole thing.