I see them remaining a demographic without a voice for the foreseeable future. Neither the fiscally conservative nor the socially conservative parts of the Republican Party can be competitive alone, and each drives away some of the other. Democrats on the other hand promise something for everyone. What cares the person who wants others to pay for his health care if someone else is getting a free education or free day care or government subsidies for his solar telephone sterilizing company? We're importing (legally and illegally) more and more poor people who want "free" stuff, and we're creating with our outsourcing and welfare programs more and more poor people who want "free" stuff. It's a double whammy, and one for which the Republicans have no real answer. If the Republicans can't beat Obama they can't beat anyone on the left, so they have a choice, they can either choose to be a permanent minority party with increasingly less relevance and power, or they can choose to become the Democrats and promise more "free" stuff, or at least more efficient handing out of the "free" stuff. I predict the latter; I think they'll be more interested in holding office than in holding whatever principles they have. Essentially you can vote for the Democrat, or you can vote for the other Democrat. Fiscal conservation will mean nothing more than 75% of the country getting government checks rather than 76%, or 75% top brackets versus 90% top brackets.
The Pubbies had better choose quickly though, or the two parties will be Democrat and La Raza.