I'd actually say neither the GOP nor the Democrats are heading towards a demographic death.
GOP isn't going anywhere because of the birth rate of religious groups, and the fact that religious immigrants tend to skew right the longer they've been in the country.
The Democrats aren't going anywhere because of the rate of attrition from religious groups. They have lower birth rates than the Republicans, which balances things out.
Balance of power is going to depend on:
1. The ratio of birth rates 2. The level of religious attrition in future generations
Look at that. It's all about the children :-)
I left fringe groups out of both sides.