Learning experience here -- the problem is NOT the new kernel. With a "workaround", the modules will compile for 3.9.1. I had forgotten that a couple of things changed earlier in the week:
(1) new kernel released, and
(2) major sid upgrades after Wheezy release.
Observing that the problem occurs prior to, or in conjunction with calling /usr/bin/vmware-gksu, resulting in no gksu request for the root password, I tried running the module-updater directly, as root, and the modules built with no problem.
I don't think the problem is in KDE -- but I used my E-17 desktop to do this. There is something in the recent Debian upgrades that is interfering with the gksu call -- that's the end of my ability to find the root cause.
Workaround:
Open a root terminal and issue
/usr/bin/vmware-modconfig --icon=vmware-player --appname=VMware
EDIT 11 MAY: On one system, the workaround did not run successfully in a root terminal. It was necessary to go to the tty console, as root, cd to the /usr/bin directory, and issue:
vmware-modconfig --console --install-all --icon=vmware-player --appname=VMware