Take a bus! It's less expensive and more comfortable.
http://www.eurolines.es/portugal.htm gives timetables & fares. There's one that departs Alicante in the afternoon via Madrid and gets you to Lisbon at 07:00. When you get to Lisbon you can take a local day tour to Fatima. :p
BTW
As you will see, daily service from Benidorm or Alicante terminates 15/09/2001, so I hope your trip is in early September (or on a Saturday)
[ 05-03-2001: Message edited by: Eddie ]