tl;dr: It is unlikely you'll be laid off, but you might need to be ready for reduced or no paycheck for a couple weeks. If you aren't a retard with money, that shouldn't be an issue.
It depends. Are you are a Fed, A Federal contractor, or are employed by a federal contract?
If you are Fed, you're fine (unless the mass beheadings actually start)
If you are a Federal contractor (that is, you are are paid directly by the federal government but are officially employed by another entity) that will be down to the term of your employment contract. You are very likely paid through October though. And even if the shut down last longer than that its highly likely you'll be returned to full employment once the taps turn back on.
If you are a employee of a federal contract, that is you are employed and paid (benefits) by a non-federal entity even if you do all/most your work for federal agencies, that will come down to the terms of the contract your employer made. Very likely they are pre-funded for the year, however the Federal entity you do your work for may request that services are suspended/contractors furloughed.
For example, if you sling hash a federal prison you are likely completely fine.
If you work in the CIA's cafeteria, you might be told you are having your hours cut back, or you might get told to stay at home and not get paid.