If by didn't backfire for R's in 2013 was in relation to the 2014 mid-terms, you're 100% correct; it didn't. But I think that had more to do with the short-term memory of the electorate. And honestly, I don't think this shut-down will have any affect on the mid-terms this year. I'd hope, if it did, that this time the electorate would properly punish those filibustering over something so trivial.
I'm aware of the polls you mention, but I think if you asked the average person an honest question such as "Should the government be shut down so that illegals aren't deported", they'd answer no. That's a straight question that even forgoes the complexities of the issue. But that's essentially what the D's are doing right now. And I hope when it all shakes out at election time later this year, that's the light it'll be seen in.
Since I've not really posted on this site much, and on this side of the board especially, I'll go on the record stating that I'm fully against illegal immigration, and 100% for streamlining the immigration policy to bring in the best and brightest. I come from this stance as someone with several friends and co-workers that immigrated her legally, and I know what they went through to do so. Every person that comes here illegally, and is granted any kind of status, is a gut-punch to those that did it the right (and extremely difficult, time-consuming, and expensive) way. We're a nation of laws; and I believe each time we allow someone to subvert those laws, it diminishes what we stand for.