Do you have 32 bit or 64 bit Vertica drivers installed? You will need the 32 bit version for Tableau.
You need to install the 32 bit Vertica ODBC drivers. To verify that you have successfully installed the 32 bit version of the Vertica ODBC, you can start the 32 bit ODBC Data Source Administrator, which is usually found in location C:\Windows\SysWOW64\odbcad32.exe on Windows 7. Now click on Tab Drivers as shown in the picture attached. You should see Vertica in the list of drivers.
Also ensure that you have the correct version of Vertica ODBC driver installed and check with Vertica that the ODBC driver version you have installed is compatible with the Vertica Server version.