I think it is increasingly likely some have so totally abandoned reality they actually believe they can win. Just like the election, reality doesn't need to be accepted until the deadlines pass and you lose, and sometimes not even then.
The thing is, the wing of the Republican party driving the continuation of the shutdown haven't really come up with a coherent idea of what "winning" would mean to them. As absolutely everyone knows, this all started because they (ultimately Speaker Boehner under pressure) refused to let a
budget Continuing Resolution bill pass the House unless it included provisions to stop the implementation of the ACA, even though that was materially impossible because of how laws actually work.
Within 36 hours they started getting violently mad whenever anyone asked them about why they shut down the government to stop Obamacare and started insisting the whole thing was about reducing government spending, because they seem to think the American populace have the memory of goldfish. Suddenly it was President Obama who pulled the plug in the first place and the shutdown hasn't ended because he's refused to pass any of the piecemeal spending bills the Republicans have been passing...
after the shutdown began.
And if that complete flip into time-traveling causality makes any sense to you, congratulations you have what it takes to be a member of the Tea Party Caucus.
Now they don't even seem to be holding onto that substantive a message, and the continuing standoff is about something like weaning the American people off of government spending or some nonsense, or their way of proving Obama
hates pandas and cancer patients, or pretty just to prove they really run the show. Which kinda sense, as best I can tell their real demand is that the Republican Party be retroactively declared winners of the 2012 election.