There's no way to know which refund will come first. The Federal and state refunds come from two different tax agencies, each doing their own thing. So it's not known how long each one will spend processing your return.
The IRS says 9 out of 10 filers who efile and choose direct deposit will get their refunds within 21 days. You can monitor it with the IRS tool mentioned below. Some returns take longer for additional processing due to specific items in the return. Some are pulled at random for more thorough investigation.
If you efiled, you can double-check with this tool to be sure the returns were efiled successfully and accepted:
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
If that showed it was accepted (or if you mailed the return), what do you see at the IRS website below for the status of your Federal refund? Click the blue button "Check My Refund Status."
http://www.irs.gov/Refunds
If that IRS tool shows that the refund has been sent, report back for more info. If it says it is still "being processed", and if it's been longer than 21 days, we can tell you how to speak to someone at the IRS to see if you can learn more about the delay.
FAQ: How do I track my state refund?