Did Carly Fiorina Betray Conservatism by Opposing the 2013 Shutdown?

Some on the right are calling Carly Fiorina a RINO for not supporting Ted Cruz during the 2013 shutdown.  Since she was not a Senator and hence we don't have a vote record for her, the evidence of her RINO-ness is an interview on CNN in which she said:

Everybody could see this train wreck coming. I actually feel badly for John Boehner. I think this is Ted Cruz and President Obama’s shutdown. I think Ted Cruz’s tactics were wrong. There’s no honor in charging a hill that you know you can’t take, only casualties, although Ted Cruz maybe got name recognition and money along the way. But President Obama wanted this shutdown. And Ted Cruz played right into his hands.

Is there anything wrong in this analysis of the 2013 attempt to defund Obamacare which resulted in a government shutdown?  It was pretty obvious to anyone with knowledge of basic arithmetic and civics that a bill to defund Obamacare would never pass.  Sure it could pass the GOP controlled House but never had a chance in the Dem controlled Senate.  And then let's not forget ye olde Presidential veto which would be almost impossible to override on such an issue (we're not even likely override it on that disastrous Iran deal which has bi-partisan opposition).  Even if every single Republican stood by Cruz, we would still have lost. Despite all of this, Ted Cruz led the charge to defund Obamacare anyway which led to a government shutdown because the House wouldn't pass a continuing resolution that didn't defund Obamacare.

A government shutdown was an obvious result and then it wasn't quite clear what the plan was to get the Democrats to cave.  So the government was shutdown, so what?  Obamacare was still, for the most part, funded due to much of it coming from mandatory, not discretionary spending.  Some government workers were furloughed, parks closed, big deal.  Cruz is no doubt brilliant but he didn't seem to think through the endgame very well.   And the Republicans were taking the blame in public opinion.  According to a CNN poll at the time, only 20% of people said that most Republican members of Congress deserved to be re-elected, compared to 42% of people saying most Democratic members of Congressed deserved re-election.  56% of respondents said the Republican Party was too extreme compared to only 42% saying the same about the Democrats.  Luckily, the shutdown was way before the 2014 election and voters forgot about it but at the time it was a complete disaster for the GOP.

Given all that, did Carly Fiorina say anything that was actually wrong?  The strategy had no hope, check.  It helped Cruz get a greater profile and probably money, check.  It helped Obama, check.  I don't remember anything about conservatism that requires you to follow a leader into certain doom, no matter how brilliant he may be.  Or to get a lobotomy so you don't question the popular kids.  I don't like thought police of any kind but I am especially disappointed when those thought police are people who claim to be for freedom and individuality.