Seems like a real mishmash - the state has 140,000 federal workers, although it's unclear how many of them would be considered essential to the workings of the nation. Mail delivery would continue, as would the air traffic control system, but the parks system would not. Some employees would be furloughed, some would continue to work without pay. When the government last shut down in 1995, the most significant effects involved services you wouldn't think of, such as getting a passport. From McClatchy:
At Yosemite, Sequoia, Kings Canyon and other national parks, visitors already inside park boundaries would be given 48 hours to leave. "Limited personnel needed to protect life and property on public lands, such as law enforcement, emergency services and firefighting personnel, will be exempted ..." said Interior Department spokeswoman Kendra Barkoff. Social Security checks would still be delivered, as would the mail. The IRS would process electronically filed returns and collect payments. But paper-filed returns would not be processed, and refunds would be held until furloughed employees return.
What's unclear is whether federally funded programs in California would be impacted in any way.
*Update: Mayor Antonio Villaraigosa tells KNX that the House budget plan "would have a $560 million impact on the city of Los Angeles." No details were offered on where he got that number, what it would include, for how long, etc. The mayor has become known for tossing around numbers - many of them preposterous.