I started my return with the online version through Gusto, but haven't paid. Instead I purchased the 2020 desktop version but need to get my data out of the online live?

If you cannot download a .taxfile from "Gusto" (whatever that is) then you will need to start over again in the downloaded version from scratch. 

You must be trying to download the pdf file.  You have to pay to get the pdf.   You need to download the data file ending in .tax2020.

You can move your Online file to the Desktop program and continue without paying for Online or needing to reenter your info.

To continue in the desktop version see this…….

https://ttlc.intuit.com/community/choosing-a-product/help/how-do-i-switch-from-turbotax-online-to-the-turbotax-software/00/26129

After you get the program installed the first thing to do before you open your tax return .tax file is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to FILE - NEW).