The algorithm field in digest authentication must not be quoted. The current version of tomcat shipped with Ubuntu 13.04 insists on this (though future versions of tomcat are more relaxed).
see comment 12.
Httpclient will thus fail to authenticate against tomcat 7.0.33 to 7.0.35, but should work against 7.0.36 and later. Note that the fix in tomcat 7.0.36 is to accommodate clients that are not conforming to the specification.