Well, here's the thing about it, at least from my perspective.
First, the government: when they strike, I cheer. I only wish they wouldn't get paid for said strike period. Overall, it impacts me very little, directly or indirectly, mainly because the duration of governmental strike isn't long enough to make much of a difference. What, they're not going to be in session for a couple weeks to make new laws? Oh, the IRS isn't going to be auditing for a while? Oh, boo! So disappointing.
</mock sarcasm>
Second, screenwriters: Hollywood is the biggest industry in the biggest state economy in the US. Furthermore, they're something like the 17th biggest economy in the world, and they produce one of the only things which we export anymore - culture and media. So this impacts us fairly substantially in terms of the trade deficit (at least with Europe) - at least I'd think so. Finally, there are more than enough 'discarded' scripts to last them years, in both movies and TV. They'll just go back and use the crappy scripts until the screenwriters stop their complaining, so anything on TV or in movies is going to be crap, with little chance of something "really good". (Thank God for reruns.)