Speaking as someone who writes campaign slogans: no.

On the shutdown: The house can and will pass a clean CR (clean as in it won't defund the ACA) with Democratic votes. This will either happen when Boehner abandons the Hastert rule or through a process such as moderate R's abandoning their party to force a vote through a discharge petition (which has already begun circulating).

On the debt limit: Same as the above, except with more urgency.

EDIT: without writing a dissertation on the current fractures in the Republican Party, the Ted Cruz wing is currently very, very hated within the party, and everyone is looking for a way out.