Need help in converting this cursor to a set based operation
Why do you need to DROP and RECREATE the table each time?  Since you're doing a DROP-CREATE, it must already exist. So, outside of the SP, recreate it as follows:

CREATE TABLE B_RPT_RC_AUDIT_ASSIGNED_TO_TEMP (      
  SEQ_NUM SMALLINT,       
  CASE_ID DECIMAL,       
  ASSIGNED_TO NCHAR(30),       
  AUDIT_STAMP DATETIME,       
  AUDIT_OPRID NCHAR(60),      
  RC_STATUS NCHAR(10),      
  PROVIDER_GRP_ID NCHAR(20),
  PRIMARY KEY(CASE_ID, SEQ_NUM)
); -- don't leave an 8 million record table in a heap!


Since all you need is merely to number the records within a CASE from 1 to N, you can use ROW_NUMBER().

ALTER PROCEDURE [dbo].[B_RPT_RC_AUDIT_ASSIGNED_TO_TEMP2_SP]
AS
  SET NOCOUNT ON;
  TRUNCATE TABLE B_RPT_RC_AUDIT_ASSIGNED_TO_TEMP;

  INSERT INTO B_RPT_RC_AUDIT_ASSIGNED_TO_TEMP       
  SELECT ROW_NUMBER() OVER (PARTITION BY CASE_ID ORDER BY AUDIT_STAMP),
         CASE_ID, ASSIGNED_TO, AUDIT_STAMP, AUDIT_OPRID, RC_STATUS, PROVIDER_GRP_ID      
    FROM B_RPT_RC_AUDIT_ASSIGNED_TO_TEMP_T2;
GO