It does not take months to complete, normally it takes 1-2 weeks assuming you follow the guidelines and prepare for the reviews accordingly. Obviously if there are security vulnerabilities found in your app it could take time to resolve so 1-2 weeks is an average and assuming you are able to resolve issues as soon as possible.
Also, if you follow the info here it will speed up the process https://ipp.developer.intuit.com/0010_Intuit_Partner_Platform/0025_Intuit_Anywhere/0040_Publishing_Your_App
regards,
Jarred