Are professors at a public university in the U.S. considered to be "employed by the U.S. government"?
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.
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.
No, grad students and faculty with NSF funding are not employed by the U.S. government. NSF funding is sent directly to the school. The school then employs the researchers itself and pays them using those funds.