I have a big workbook with a lot of data. In one sheet I have a table. This table is used for many Pivot tables used in other sheets, which are also used in other sheets.
This might be a helpful workaround. I have successfully done this but it may require a bit of rework and not be the exact answer you expect. (I am using Excel 2010).
The reason for a workaround is I assume this is for a regular table (not a pivot table) as the source table. Unfortunately, I don't believe the switching connection options work for regular tables in Excel 2010.
Recreate a new table just below the other in the same worksheet by going to the Data tab > Get External Data > Existing Connections
Select your data connection (assuming it has been created) then select how you want to view the data. ie: Table
Place in your existing worksheet. Use your old table as a reference to reconnect all the connections to your other sheets, then delete the old table.
At this point, I find it easier to rebuild/copy those existing links to the new table with external data.
The good news: If your source table is a pivot table or pivot chart with an existing connection, you can easily change the table to have an external data connection (and switch between data connections).
For a pivot table with an existing connection you wish to change, select a cell in the table. In the ribbon above in 'PivotTable Tools' > Options tab > Change Data Source, you will be able to select this and reconnect to another source under 'Choose connection'.
For a pivot table with static data to introduce a new connection, I would suggest a similar workaround above.
I hope this works for you.