Accepted in TurboTax just means the government has received your return. It can range from a span of just a few days up to about 3 weeks to see a move to approved on the IRS and/or your state's websites when tracking your status. The next step is for them to start reviewing/processing your return and then approve your refund. Just keep an eye out on their website for updates.
And you can use your State Department of Revenue's website to check status of
state tax refund. Choose your state here
How do I track my state refund? and it will give you steps to track the status.
