"Patrick Swayze was signed to play Quaid when the movie began preproduction in Australia with Bruce Beresford as the director. However, early in preproduction, Dino De Laurentiis' company went bankrupt. After Arnold Schwarzenegger heard about this, he persuaded Carolco to buy the script for him."
So Yes, the original choice was Patrick Swayze.
Some other choices were;
"David Cronenberg was attached to direct but wanted to cast William Hurt in the lead role" Wikipedia
Among other chocies were Christopher Reeve, Jeff Bridges, Matthew Broderick and Richard Dreyfuss
Complete information is also present here: Cast List