There is no reason that it will not work now. 

I downloaded it again today and it still won't open.

Won't open of won't install?  What are the symptoms you see?

https://ttlc.intuit.com/community/installing/help/turbotax-for-the-mac-installation-troubleshooter/0...

https://ttlc.intuit.com/community/troubleshooting/help/turbotax-for-mac-won-t-open-when-installed/01...

The app downloads well.  I get a message that Apple finds no malicious software. When I try to open the app I get a message saying " Please wait while we verify everything is up to date..." and then it quits.

if you get the message "TurboTax cannot be opened because Apple cannot check it for malicious software" then that is caused by the Apple "Gatekeeper" introduced with OS X 10.15 (Catalina).

That has nothing to do with TurboTax and will happen for any application not purchased from the Apple Store.

See this Apple article on this: https://support.apple.com/en-us/HT202491

And this TurboTax help article: https://ttlc.intuit.com/community/troubleshooting/help/turbotax-for-mac-won-t-open-when-installed/00...

For older Mac systems when TurboTax will not open.
See:

Be sure that System Preferences -> Security & Privacy -> General -> Allow apps downloaded from App Store and identified developers is checked.

Go to the Applications folder and select the TurboTax application in the Finder and right click with the mouse (or control click) ans select the top "open". That should force the first open. After that it should open normally.

https://ttlc.intuit.com/questions/1899267-administrator-rights-mac

I installed the 2019 version on Big Sur and it appears to run fine.

My problem is that Turbotax Deluxe 2020 takes a very long time to open. It seemed to install easily. I timed how long it takes to open - 6 minutes 20 seconds. At that point my data file hasn't opened yet - that takes another 4-5 minutes. Once open, the data file works normally. Is there a problem with Turbotax & Mac OS Big Sur?

Never heard of that.   Suggest a restart of your computer and/or use the Utilities -> Activity Monitor to see CPU usage and memory usage.  Other running applications might be hogging the processor and/or using the available memory that forces memory swaps and extreme slow running.

Has anyone in this thread installed Turbotax Home & Business 2020 on a Mac w/Big Sur and, if so, does it work????

I'm having the same exact problem and it's driving me crazy. 

if you get the message "TurboTax cannot be opened because Apple cannot check it for malicious software" then that is caused by the Apple "Gatekeeper" introduced with OS X 10.15 (Catalina).

That has nothing to do with TurboTax and will happen for any application not purchased from the Apple Store.

See this Apple article on this: https://support.apple.com/en-us/HT202491

And this TurboTax help article: https://ttlc.intuit.com/community/troubleshooting/help/turbotax-for-mac-won-t-open-when-installed/00...

For older Mac systems when TurboTax will not open.
See:

Be sure that System Preferences -> Security & Privacy -> General -> Allow apps downloaded from App Store and identified developers is checked.

Go to the Applications folder and select the TurboTax application in the Finder and right click with the mouse (or control click) ans select the top "open". That should force the first open. After that it should open normally.

https://ttlc.intuit.com/questions/1899267-administrator-rights-mac

same problem here

same problem here. Installs but doesn't open. Have Mac OS Big Sur v11.1

I installed TT 2020 on two different Mac's.  One running Mojave that took about 3-5 mins. to install using the disk and the other running BiG Sur took 30 mins.  On Big Sur it wants to load every file file from the disk very slowly.  When done all works but why it is so slow is beyond me.