Cardinal Dolan has my prayers but I think this is a huuuuge mistake.
You can read his whole explanation here but here's a nugget:
Some have told me the invitation is a scandal. That charge weighs on me, as it would on any person of faith, but especially a pastor, who longs to give good example, never bad. So, I apologize if I have given such scandal. I suppose it’s a case of prudential judgment: would I give more scandal by inviting the two candidates, or by not inviting them?This event will be used by the Obama campaign to further its chances at re-election.
No matter what you might think of this particular decision, might I ask your prayers for me and my brother bishops and priests who are faced with making these decisions, so that we will be wise and faithful shepherds as God calls us to be?
In the end, I’m encouraged by the example of Jesus, who was blistered by his critics for dining with those some considered sinners; and by the recognition that, if I only sat down with people who agreed with me, and I with them, or with those who were saints, I’d be taking all my meals alone.
I'll probably write more about this later and Pat probably will as well but I just wanted to get this up for your perusal.