Turbotax will keep your returns for 7 years. So no need to worry just yet. However, its always advisable to have everything backed up. You never know what might happen. I totally understand not wanting to print all that out. However, you have other options such as backing them up somewhere else online. Many people use Google Drive, or Dropbox. If you're not comfortable with that option, you can get a usb stick or portable hard drive that can be password protected, and store all your vital documents there. No rush to decide, as you do have the 7 years, but it is definitely something important to consider.
Currently returns from 2015 and later are accessible in TurboTax. From your Tax Home screen, scroll down and select Your tax returns & documents. Select the year you want, then select Download/print return (PDF).
