You forget about travelling time.
If you go by bus (and I mean public transport) I will take you about 10 hours to get from Jeddah to Aqaba in Jordan. From Aqaba to Amman it will be another 4 hours. From Amman to the Syrian border it will be 1 hour and then another 2 hours to get to Damascus.
That is just the time you spend on the bus, this does not include the time you need to wait for the shared taxi or the bus to leave. For example: When I went from Wadi Musa to Aqaba took the minibus from Wadi Musa to Maan and then wanted to go on to Aqaba. I sat in Ma'an for 3 hours waiting for the departure of the bus to Aqaba.
Damascus to Turkey is even worse. It takes about 14 hours by direct bus to get from Istanbul to Gaziantep or Adana, the 2 big cities near the Syrian border. From there to Latakia it is about 2-3 hours and another 6 hours from Latakia to Damascus.
Considering the travelling time and your timeframe I recommend that you skip Turkey. It would take you too long to get there unless you fly.
See this thread:
http://www.travellerspoint.com/forum.cfm?thread=61839
Especially look at what magykal1 wrote:
Quoting magykal1
I reckon in 16 days you could just about fit in Beirut-Baalbek-Damascus-Palmyra-one of the Crusader Castles-Jerash-Amman-Petra.
[ Edit: Edited on 21-Jun-2009, at 06:09 by t_maia ]