Yes, they can in California. However, you can have a judge review this to ensure that it does not leave you out in the cold, which is not the point of our judgment enforcement rules. You should file with the levying officer a claim of exemption to both the garnishment and the bank levy. There is no charge for this, but you will need to provide your household financial information, if the plaintiff/judgment creditor decides to challenge your claim, so the judge can review all of it. I have on Avvo a legal guide to reduce wage garnishment. See the link, below.
I am also concerned at how this came to become a judgment? Were you properly served? Did you file papers opposing the lawsuit? How and when did you first learn of this lawsuit and/or judgment? If this wage garnishment or bank levy were the first times that you learned of this lawsuit, then you were probably not served properly and may (if you act promptly) be permitted by the court to set aside the judgment, which would relieve you of all enforcement efforts and probably get the levy and garnished funds refunded in full. An invalid judgment should not be enforced by the courts, but this is where it gets difficult, and an inexperienced or general practice lawyer might not succeed.