I need historical data related total births and deaths for US state and county wise so that I can trace the changes in trends
This could be a good resource: the US Vital Statistics Data: Data Access - Vital Statistics Online
Here is the same data set, except formatted in different ways that are easier for Tableau to digest. NCHS' Vital Statistics Natality Birth Data
With this, you will still want to get the users guide from Data Access - Vital Statistics Online to understand the various columns.
Retrieving data ...