The IRS says that they pay 9 out of 10 refunds within 21 days. If you mailed your tax return "around the end of May" it might not be 21 days yet. Mailed returns take a little longer, and returns with EIC often take longer, so you may be the 1 out of 10 that takes longer than 21 days.
We can't give you an update. Your refund comes from the IRS, not from TurboTax. No one here in AnswerXchange or in TurboTax can check the status of your refund. Starting about 4 weeks after you mailed your tax return you can check the status yourself by using "Where's My Refund?" at the following link on the IRS web site.
http://www.irs.gov/Refunds
See the following links on the IRS web site for more information about refund processing time.
http://www.irs.gov/Refunds/What-to-Expect-for-Refunds-This-Year
http://www.irs.gov/Refunds/Tax-Season-Refund-Frequently-Asked-Questions
