107.3e Sometimes X appears in the text of a spell or ability but not in a mana cost, alternative cost, additional cost, or activation cost. If the value of X isn't defined, the controller of the spell or ability chooses the value of X at the appropriate time (either as it's put on the stack or as it resolves).

It will be perfectly reasonable to entwine the spell and as it resolves sac the creature, gain the 3 life, pay (your life total-1) and look at that many cards from the top of your library to put one into your hand.  It will not be until you've done this that you or your opponent can respond to any of the actions taken during the resolution. 

Also note the order of the trigger as well.  You must fully resolve the Entwined spell before you can search your library for the enchantment.  This means if you're tutoring through the top 15-20 cards and ALL of your Near Death Experiences are among them if you don't choose one to put into your hand they will all be exiled before you can search with the Rector.