Yes, there actually were plans at one time for a Red Dwarf American Series, but most serious fans of British Comedy don't consider the fact that it failed a sad one since as a general rule most of the humor is lost in translation (like "Cosby", which was based on "One Foot in the Grave")or else made something horrible and unwatchable (like NBC's "Must See TV" classic "Men Behaving Badly").
Rumors have been flying around the net about this for years, but we do know that executives pushed to make Lister a more appealing leading man, instead of the unwashed slob we all know and love and wanted to give him a different love interest every week, as opposed to Lister's rather romantic devotion to Kristine Kochanski! There were also plans to take the "H" off Rimmer's head and replace it with a red (then silver) circle. Also, Cat would be a woman (a move probably made to attract the young, horny sci-fi Catwoman loving male audience).
Interestingly enough, Robert Llewellyn was going to reprise his role as Kryten. Chris Barrie was offered the chance to play Rimmer, but turned it down. Also interesting is that Jane Leeves (who would later become "The Virgin" on "Seinfeld" and Daphne Moon from "Fraiser") was going to play Holly and Terry Farrel (who would go on to becom Dax on Star Trek: DS9) was going to play the female Cat.
The script to the pilot is here. I should warn you that reading the pilot may cause severe irritation at the American TV executives.
Red Dwarf USA Pilot: Essentially "The End" with Americanized Jokes (i.e. Rimmer comapres death to an Amish Bachelor Party instead of going on Holiday with a bunch of German Tourists).