Try clearing your cache and deleting cookies from your browser and then try signing in again. TurboTax saves everything as you go, so all of your information will be there when you sign back in.
Your browser stores recently visited web pages as temporary files in a cache, which enables the pages to load up more quickly when revisited.
However, a full or corrupted cache can cause various problems in TurboTax, so sometimes you need to clear your cache (that is, remove these temporary files).
Here are the official instructions for the most popular browsers:
Apple's official support site doesn't appear to contain instructions for clearing the cache in Safari. Your best bet is to search the internet for clear Safari cache or similar search terms.