Can I exit without saving data I entered today?

Using the online editions? No, the data is saved as it is entered.

You can always Clear and Start Over.

The Online version saves as you go, so when you exit it will automatically save your data.  You can use the clear and start over option to remove any data you entered, as long as you haven't submitted payment, deducted the TurboTax fee from your refund, or registered.