Okay, here's exactly what I did:
cd /usr/local/freeswitch/conf/directory/default
cp 1001.xml 2319.xml
perl -pi -e 's/1001/2319/g' 2319.xml
cat 2319.xml

<include>
  <user id="2319">
    <params>
      <param name="password" value="$${default_password}"/>
      <param name="vm-password" value="2319"/>
    </params>
    <variables>
      <variable name="toll_allow" value="domestic,international,local"/>
      <variable name="accountcode" value="2319"/>
      <variable name="user_context" value="default"/>
      <variable name="effective_caller_id_name" value="Extension 2319"/>
      <variable name="effective_caller_id_number" value="2319"/>
      <variable name="outbound_caller_id_name" value="$${outbound_caller_name}"/>
      <variable name="outbound_caller_id_number" value="$${outbound_caller_id}"/>
      <variable name="callgroup" value="techsupport"/>
    </variables>
  </user>
</include>

Then I logged into fs_cli, pressed F6 (which does "reloadxml") and then I set up my x-lite:
Display Name: Test
User name: 2319
Password: 1234
Authorization user name: 2319
Domain: 10.15.0.91

It registered just fine as can be seen by the output of "sofia status profile internal":
<snip>
Call-ID:        MzRiOGI4NTA2YjA0ZTkzMDYwZjA3MTlkZGQ3ZjNhMjg.
User:           2319@10.15.0.91
Contact:        "Test" <sip:2319@10.15.0.124:41680;rinstance=09c51f8aa23d6738>
Agent:          X-Lite release 1014k stamp 47051
Status:         Registered(UDP)(unknown) EXP(2009-12-03 13:41:38)
Host:           freeswitch1.yt
IP:             10.15.0.124
Port:           41680
Auth-User:      2319
Auth-Realm:     10.15.0.91
MWI-Account:    2319@10.15.0.91

So, most likely you've got an issue with the XML file itself or the configuration on your SIP device. Double check the username and auth username values. If need be delete your 2319.xml file and start over.

-MC