I think Obama and company need to be resolute BUT need to communicate better particularly to the man-in-the-street their rationale for this behavior.
What the Cruz and Tea Party grouping are doing amounts to political terrorism in that their approach is one of if we cant get what we want well destroy it all and where the bomb is basically Americas creditworthiness and reputation on the global stage.
Theres a term for this Brinkmanship which defines a situation where one group pushes to very edge on the basis that they know the other group will fold. This can work if the other group DOES fold, but is downright dangerous if not.
What Obama & co need to make clear to the population is that this situation IS, IN FACT, POLITICAL TERRORISM and that the US IS AT WAR WITH TERRORISM IN ANY FORM!
To submit to what is essentially blackmail would also set a precedent and open the US government to more and more similar ultimatums in future every time some group does not get their way, then this type of situation will recur.
The current communication strategy of Obama & co appears to be woefully inadequate when viewed from the position of the man-in-the-street as the messages are pitched at an audience that understands economics and not the level of one who understands putting food on the table.
Until the grass roots supporters of the Tea Party grouping fully comprehend where the Tea Party is actually taking them, they'll continue to follow the rhetoric....