I spent a few hours yesterday trying to massage my text file of quotes into a JSON file to import and even after two converters did their thing, it would say it imported the right number of quotes but nothing was there. In order to delete all of them, I found I had to deactivate and delete the plug-in before trying again. In desperation I manually entered one quote and exported it to see how the file varied from that I had.
Turned out the "field" names - quote, author etc were capitalized by the converters because I'd entered a line with header info that was capitalized and the exported file was all lower case. After grepping all the field names I imported again. This time it managed to import but everything was marked private. I deactivated and deleted a last time and did a global replacement on my JSON file to add the final field for each quote showing public.
My suggestion is to do the manual entry trick before starting the data-massage process if you have a lot of quotes. I've done the thrashing so you don't have to!