This is mainly a user community forum, not a direct route to TurboTax Support, but we can suggest some things.
Your deadline of July 10 is today. What tax year does your letter concern?
What type of IRS letter? There should be a CP or LTR number in the right corner. What is the IRS alleging and wanting you to do? (this is a public Internet forum, so don't post any personal info.)
I see you are using the Live Premier product. If you are having trouble timely reaching a tax expert at TurboTax Support, you can also phone the TurboTax free Audit Support Center. Tell them of your situation and the deadline, etc. To get the phone number, go to the page below, click the blue "Get Help" button and follow the prompts.
https://support.turbotax.intuit.com/irs-notice/audit-support/
You can also contact TurboTax general Customer Support and tell them about the trouble timely scheduling a tax expert, and perhaps they can either assist you or hook you up with a tax expert.
Hours are 5AM-5PM Pacific (8AM-8PM Eastern) Monday-Friday.
FAQ: What is the TurboTax phone number?
https://ttlc.intuit.com/community/using-turbotax/help/what-is-the-turbotax-phone-number/00/25632
Did you just make the appointment tonight with your tax expert? If it's after hours, and they are closed when you try to schedule one, then sometimes it gives a distant appointment date. For some reason, people may get a better and faster appointment date scheduled if they go through that scheduling process during the hours they are open. But since your deadline is today July 10, you should contact TurboTax by one of the methods above.
Or did you happen to purchase the optional Audit Defense or MAX product? If so, we can tell you how to contact the third-party company that handles those (intuit.taxaudit.com) .