What are the chances your federal tax refund will come sooner than what they say?
E-file is quickest for refund.
The IRS is pretty good at saying when it comes. You can check here: https://sa2.www4.irs.gov/irfof/lang/en/irfofgetstatus.jsp The info on that site is going to be the best site. If there is any problem like you were rejected or they need more info the site will let you know.