I'm seeing this question very late, but have two possibly useful suggestions for drawing posets:

1. My favorite way to automatically draw large graphs with unknown structure is GraphViz. See http://www.graphviz.org/
   With some work, this can be made to give poset diagrams. That's one of the good options for output of Stembridge's Poset package for Maple, as mentioned in one of the other answers. (But GraphViz is open source software, which seems like a significant advantage to me.) Looking at the source code of Stembridge's package might be a good place to start in figuring out which GraphViz options to look at.

2. GAP with the XGap (for Unix/Xwindows) or my own Gap.app (for Mac) front-end has code which allows manipulating Hasse diagrams of posets. I have found it useful for making good diagrams of small to medium size posets. I realize that the question asks about large posets, but include this for completeness.
   For good results, GAP requires you to specify the position of the vertices (and automatically draws the edges for you), so it helps if you have some idea of the structure of the poset.
   (I can share an example or two of presenting poset diagrams with GAP, if it would be helpful.)