Each month is set up as a different dimension (column) in the data. In Tableau, these discrete dimensions are separate and you can't draw a line chart because Tableau needs a continuous set of values.
You need to reshape your data to look more like this:
Date Dimension 1 Dimension 2 Dimension 3 1/1/12 272 8,026 2/1/12 349 8353 3/1/12 289 8642
This Knowledge Base article should help, and at the bottom of it is a link to an Excel add-in that can make life easier.
If this is something that you would need to do every time the data refreshes, you might want to look into Custom SQL to do the reshaping for you.
Thanks Jonathan! That answers it. And thanks for the link to that add-in.