The nature of the GOP's demographic-electoral problem is three-fold. First, the challenge of trying to evolve and adapt is itself limited by demographics because the GOP's older and whiter residual white minority coalition is simply less amenable to the sort of changes it would take to modernize the party. Second, so many of the figures within the party who might be able to lead a center-right revival have been beaten in recent cycles, with the old Ford/Dole/Rockefeller wing decimated by the 2006 and 2008 cycles. (Relatedly, it doesn't help when people like Frum are cast out from their intellectual circles.) Finally, it is simply not in the nature of conservatism to foment change or be out in front of demographic and social changes: Conservatism works best as a reaction to--not necessarily reactionary, but a reaction nonetheless--to oncoming, rapid changes.
Andrew Gelman throws a couple grains of salt at Teixeira's analysis.