[dba-SQLServer] SQL Server 2005 - Executing query. Waiting for response from data source.

I have related tables in SQL Server.  Whenever I try to build a view where I
link (drag and drop, inner join) the related FKs between the two tables, I
get:
 
"Executing query.  Waiting for response from Data Source."
 
It eventually times out, rather quickly in fact, perhaps 30 seconds or so.
Management studio returns an error message like:
 
SQL Execution Error
 
Executed SQL Statement: SELECT dbo.tblPeople.PE_ID, ,,,
 
Error Source: .Net SQL Data Provider
Error Message: Timeout Expired.  The timeout period elapsed prior to
completion of the operation, or the server is not responding.
 
The query it attempting to join two tables, each containing 53 million
records, on a common foreign key, which should result to a one to one result
pulling the PK from the respective table.  The idea is to then write those
table PKs out to a m-m table to cause these two tables to be related via the
m-m table.
 
The used in the join FKs are indexed.  
 
It seems that I am truly running into a timeout but I am not sure where.
When I select the database and select options, query execution is set for 0
(no timeout).  Any clue why (or if) I am timing out?
 
John W. Colby
Colby Consulting
www.ColbyConsulting.com