Apparently, BioWare and Electronic Arts had planned a first person shooter based on the Mass Effect license. The game was called Mass Effect Team Assault, and it was worked on by BioWare's Montreal studio in 2010. The multiplayer in Mass Effect 3 is what remains of that project.
According to Geoff Keighley in the iTunes app The Final Hours of Mass Effect 3, "The goal was simple, to create a standalone multiplayer experience in the Mass Effect universe that would mix the play styles of Unreal Tournament and Battlefield 1943 — and likely be released as a downloadable game."
As the screenshots show, drivable and flyable vehicles would have been a part of the game.
Mass Effect Team Assault was in development for four months, and the prototpe was submitted in March 2010. While the BioWare heads liked it, they decided it should be folded into a co-op mode for Mass Effect 3. While the engine itself couldn't be used, the multiplayer turned out to be fairly popular.
Mass Effect 3 was released last week on PC, Xbox 360 and PlayStation 3.