The "Run, cactus kid, run" campaign, created by Mother, comprises three humorous 30-second TV spots shot in the style of the film 'True Romance'. It continues the strapline "for people who don't like water".
One spot shows the pair, who only drink Oasis and don't like water, telling the girl's mother that she is pregnant.
The mother reacts badly, calling cactus kid a "freak" and the couple drive away together.
A fourth spot will appear online with alternative endings so that users can vote on how the story ends.
The Advertising Standards Authority has received 11 complaints so far about the ad from people who objected that it is offensive because it normalises or glamorises teenage pregnancy and that it is also irresponsible for suggesting people should drink Oasis instead of water.
Some people also questioned whether the girl is a minor and whether the ad has been scheduled appropriately.
The ASA is considering whether to investigate the complaints and expects to make a decision next week.