Do you think the Republicans are still going to claim to be pro-Defense when close to 1.5 million troops suddenly found out that their pay checks have been frozen?
I would think so...it hasn't necessarily burned them at all during past shutdowns.
I've been alive long enough to remember a few shutdowns. How the "script" usually goes is that the two factions mutually label the other as the "culprit", and blame the residual effects on "see, look what's happening, if those other guys just would've given us what we wanted and stopped being stubborn, this could've all been avoided".
...the end result is that it really doesn't impact allegiances.
The take away will end up being
Most republicans will think "if those Democrats would've just conceded on some of their spending endeavors, this wouldn't have have happened"
Most democrats will think "if those Republicans would've just stopped being so stubborn about the cuts they wanted, this could've been avoided"
Rinse...repeat...
The 2013 shutdown (that lasted over 2 weeks) followed that pattern.
Perhaps this is a wild theory, but how imagine things happening is that:
congress/senate does their little song & dance with the shutdown up until a point, and when it gets to the point where private sector corporate entities (IE: their donors) start having their own profits put in jeopardy, that's when some of these elected officials start getting some phone calls to the effect of "okay, you've had your fun...now quit messing around get this signed or we'll find someone else to donate to next time around".
Again, perhaps just a wild theory, but I can think of no other explanation for why the 2013 shutdown shaked out the way it did. Staunch deadlock and refusal to compromise on ACA provisions...to the point where they were willing to furlough 800,000 federal workers (and make another million work without pay) to "prove their point". But then seemingly out of nowhere, Boehner withdraws all objections, and holds a vote and passes the budget the next day. Obviously nobody can read their minds, but to me, that sudden loss of any and all resolve sounds like the work of people who know where their bread is buttered, and just got a phone call.