What your employer can and can not claim varies by state. Some places such as California have fairly good (for the employee) laws on this because the issue has been tried in court several times.
But you really don't want to rely on the default interpretations of things by courts. Ideally you would clarify your position with your employer first. The Australian Sysadmin Guild (SAGE-AU) has some sample clauses they recommend inserting into contracts if you are doing Open Source work. Please note that the clauses are written with respect to Australian law, so you probably can't just cut and paste them (unless you are in Australia), but at least it provides a base to think about.