My application is setted with pt-BR culture (Date is dd-mm-yyyy) in web.config:
As someone who does a lot of work with US companies, I've had a lot of experience with date issues.
My best advice is to choose an unambiguous format when transmitting.
dd-MMM-yyyy
and
yyyy-MM-dd
Are safe bets, and will be successfully parsed by DateTime.Parse(obj).
If changing the date format is not an option, you should look at DateTime.ParseExact, which allows you to specify the exact format string you are after.