Dear Ashley,
In the asset id you need to include the full path to the asset (if you uploaded the shapefile to a Google Earth Engine asset) or the ID (not the name) of the fusion table.
1. For the asset path it should be something like users/YOUR_GMAIL_USER/NAME_OF_THE_ASSET , e.g. for an asset in the root folder of the assets called plantations :
users/collectearth/plantations
2. For a fusion table you need to use ft:FUSION_TABLE_ID , the id of the fusion table can be found on the URL of the Fusion table. e.g. my test fusion table https://fusiontables.google.com/DataSource?docid=**1zlbOD-QPIEF-cNw-eclaIrze70MXN6jJG4GRRO0X** [https://fusiontables.google.com/DataSource?docid=**1zlbOD-QPIEF-cNw-eclaIrze70MXN6jJG4GRRO0X**][1] . So in this case you would use **ft:1zlbOD-QPIEF-cNw-eclaIrze70MXN6jJG4GRRO0X**
Hope this clarifies the issue!
[1]: https://fusiontables.google.com/DataSource?docid=1zlbOD-QPIEF-cNw-eclaIrze70MXN6jJG4GRRO0X