How will the shutdown change 2014 election results?
There are basically two ways a national swing can happen in Congressional races.
One is direct: voters shift from one party to the other. That one almost always happens against an incumbent party, generally against the party of the president. It's of course technically possible for it to go the other way, but it's highly unlikely. And the shutdown is especially unlikely to produce any such direct electoral action -- because even if voters really do care, and even if swing voters blame Republicans, it's unlikely that they're going to still be thinking about it by next November. So I wouldn't pay much attention at all to current polling for its predictive value (and I think I've already mentioned that I wouldn't pay any attention at all to the recent PPP poll in competitive Republican-held House districts; I think Sam Wang is totally wrong to believe that there's anything predictive there at all).
So a direct effect of voters punishing Republicans is highly unlikely (it's actually probably more likely that voters would punish Democrats if there are long-lasting economic effects, although it's probably true that elite opinion placing the blame squarely on the GOP probably would neutralize that).
However, there's also a potential indirect effect. Conventional wisdom in House races (and to a lesser extent Senate elections) can be self-fulfilling. If party actors on both sides believe that it's going to be a good cycle for one party, then that party will recruit better candidates, suffer fewer retirements in tough-to-defend districts, and have plenty of resources available. And since candidate quality is extremely important in House elections, that's going to swing seats in the favored party's direction -- even if voters don't have any connection to this "trend" at all.
There's a real chance that this indirect effect will really show up this time around, and now a bit of evidence -- reported in an excellent item from Greg Sargent -- that there are already some real candidate recruitment effects on the Democratic side. To be sure, DCCC claims should be taken with a grain of salt, especially with no actual candidate names attached. But then again the polls showing Democrats "winning" the shutdown are really only a couple of days old.
I'll note one other thing. The almost-universal interpretation of the 1995-1996 shutdowns also should work for Democrats, in two ways. First, it's one of the reasons that neutral reporters are likely to interpret this one the same way (just as reporters were likely to believe that a Republican landslide was possible or even likely during the 2010 cycle). And, second, party actors are, even beyond the reporting, probably set to interpret it that way.
On the other hand: it's also a midterm election, and "everyone" knows that midterm elections are bad for the party in the White House -- which means that any effects from the shutdown will be competing against effects from that other piece of conventional wisdom. Not only that, but there's probably a more general conventional wisdom right now that all midterms are good for Republicans, and all presidential years good for Democrats (it's mostly bunk, but what matter here is what people believe). So that, too, is something pushing all those bright young district attorneys, state senators, and local celebrities towards running this time if they are Republicans, and against it if they are Democrats.
All of which is to say that it's likely that the best Democrats can realistically hope for is for indirect effects of the shutdown to cancel out the other indirect effects out there and produce a push election, or maybe small gains. Nothing is impossible, of course, and if this winds up being significantly worse than the 1995-1996 shutdowns then we will be in uncharted territory of sorts. But I'd be very surprised by a large Democratic win in 2014.