Also, is a grad student who is being funded by an NSF grant considered to be "employed by the U.S. government"?
I ask because I'm submitting a paper, and I have to state whether or not all authors are "employed by the U.S. government".
The reason this question is asked by journals is that except in some limited cases, the US government may not, by law, hold the US copyright in a work created by its employees, and, therefore, cannot transfer it to the publisher of the journal as is traditionally done in most academic publishing agreements. As such, the journal can't ask those authors who are US government employees to sign the copyright transfer and must use a different agreement. If one or more of the authors is not a US government employee, then those authors will still need to make the transfer.
Employees of US state governments, which includes most public university employees in the US, do not have this limitation, and can make the copyright transfer or other licensing arrangement that the publisher requires.
The question is really asking about employees of the federal government. At least, whenever I've seen a question like this, that is what they wanted to know; and this is the usual meaning of the words "U.S. government" in the American context.
As a rule, if you don't know whether you're a U.S. government employee - then you're probably not. An easy way to find out if your coauthors are government employees is to ask them.
The federal government does operate a handful of academic institutions (e.g., the Naval Postgraduate School) and there are other federal employees who publish regularly (e.g., scientists at NASA). There are lots of U.S. institutions which are run or chartered by state governments, and this category represents the majority of "public universities" in the country. Whether or not professors there are considered employees of the state - in most cases they probably are - they are still not federal employees. (Well, unless they happen to be on temporary assignment to NSF as a program director, or something.)
As stated in the sibling answer by Oswald Veblen, receiving money through a federal grant does not make you a federal employee.
In almost all cases, no, they are not. The vast majority of public universities in the U.S. are owned and operated by the individual state governments, not the U.S. federal government. Within the U.S., the state governments are considered to be entirely separate legal entities. In most (but apparently not all) cases, employees of state-owned universities are considered employees of that particular state. The exceptions where a public university professor actually would be a U.S. federal government employee are professors at the handful of universities actually owned by the federal government, such as the various military academies, as well as dual-employees of both a university and some part of the federal government, such as a federal government research institution. One of my advisors, for instance, is an employee both of my university and of Oak Ridge National Laboratory, so he's an employee both of the State of Tennessee as well as of the U.S. federal government.
It is not clear that public university/college employees are officially considered state employees by the respective states. In Minnesota, for example, the University of Minnesota faculty are, apparently, not considered to be state employees.
Among other aspects that make this seem reasonable, the fact that the state supplies only a small fraction of the funding contributes.
The department secretary or perhaps a grants officer at your university should be able to give you guidance on these sorts of things. Aside from the particular problem of federal employment, you might have to credit grants and authors in a way that the journal doesn't require or track.
As a graduate student, the department secretary should be your best friend. They know how everything works where the academic staff might not (because they rely on the administrative staff).