The idea of "tummy time" is so new - it's only because most babies are forever stuck on their backs now, in car seats so much of the time even while OUT of the car (it's so common for babies to be put into the car seat carrier, and then REMAIN in the car seat carrier once they get to their destination where the mom takes the car seat carrier and plunks it into the stroller, and then the baby is fed in the carrier, etc.).
I saw a few other moms give this advice already, but I just really want to support what they said --> if you carry your baby in a soft carrier (like a sling or a soft-structured carrier or a wrap), instead of transporting your baby everywhere in the car seat, then you don't have to worry about tummy time - seriously!
Here are a few links w/ more pics and information:
http://peppermint.com/guide.html
http://www.cottoncradles.com/stylesdescription.htm
http://en.wikipedia.org/wiki/Babywearing
So... instead of keeping babies in plastic baby buckets all day, simply leave the car seat carrier where it's intended to be: IN THE CAR! And just take your baby with you, held close to your body, and breathe in the sweet smell of your baby's head. Then you practically never have to worry about tummy time (assuming your baby is developing normally).
P.S. - Enjoy their being so small, so portable, and their being right there with you - this is a short time in their life! Soon enough they'll be running everywhere. :)