If the error was raised while you are in BIDS, then ajdams solution will not work as it only applies to errors raised while running the package from the SQL Server Agent.
The primary problem is that SSIS is struggling to resolve the meta data. From its stand-point, the ## tables don't exist since it can't return the meta data for the object during the pre-execution phase. So you have to find a way to either satisfy its requirement that the table already exists. There are a few solutions:
Don't use temporary tables. Instead, create a working database and put all your objects in it. Obviously, this probably don't work if you are trying to get the data on a server where you aren't a dbo like a production server, so you can't rely on this solution.
Use CTE's instead of temporary tables. This works if your source server is 2005/2008. This won't help if the source server is 2000.
Create the ## table in a separate Execute SQL command. Set the connection's RetainSameConnection property to True. Set DelayValidation to true for the data flow. When you setup the data flow, fake it out by temporarily adding a SELECT TOP 0 field = CAST(NULL AS INT) to the top of the stored procedure that has identical meta data to your final output. Remember to remove this from the stored procedure before you run the package. This is also a handy trick for sharing temporary table data between data flows. If you want the rest of the package to use separate connections so that they can run in parallel, then you have to create an additional non-shared connection. This evades the problem since the temporary table already exists at the time the data flow tasks runs.
Option 3 achieves your goal, but it is complicated and has the limitation that you have to separate the create ## command into another stored procedure call. If you have the ability to create stored procedures on the source server, then you probably also have the ability to create other objects like staging tables and this is usually a better solution. It also side-steps possible TempDB contention issues which is a desirable benefit as well.
Good luck and let me know if you need further guidance on how to implement step 3.