The javax.ws.rs package in particular is in a file called jsr311-api-XYZ.jar (XYZ being the version). It -and all the other ones that are needed to use Jersey- is available from the Jersey download page.
Thanks, that explains it. The Jersey download page is pretty confusing; I didn't want to have to build the JARs myself.
In fact, I appear to have found it. Where it says, "A zip of Jersey containing the Jersey jars, core dependencies (it does not provide dependencies for third party jars beyond the those for JSON support) and JavaDoc." Using those JARs I have eliminated the errors.