SSMS Object Explorer Details causes deadlock while job is running
In my case, I was able to solve the problem by reducing the size of the transaction in the stored procedure, ala the comment provided by @Aaron Bertrand.  The entire stored procedure was wrapped in one begin/end transaction.  As the stored procedure progressed, my management studio instance would lock up.  Reducing the transaction to just the critical inserts/updates, and adding some error handling, eliminated the problems I was having with SSMS.