A few things to note: You may want to import your GEDCOM into a desktop program first to check it for errors, or so that you can break it up into smaller branches, and upload small files (always recommended!) You can download free versions of RootsMagic or Legacy Family Tree for this purpose.
Also note that if your resulting GEDCOM from a GENI download is a zipped file, it will need to be unzipped before adding to either a genealogy program or to WikiTree, so that the extension is just .ged, and not .zip. Try right clicking on the file and seeing if Unzip or Uncompress is an option.