Republican strategist Mike Murphy, who worked for John McCain in the 2000 Presidential campaign, has written an article for TIME Magazine, in which he predicts an "Ice Age" for the GOP unless they can change their appeal to the electorate.
A careful study of the 2008 Presidential election demonstrates the trouble the Republican are in.  They lost the growing Hispanic vote by a wide margin. They lost the younger voters, who are more than ever socially liberal, even if many are economically conservative. They lost a growing percentage of suburban voters on the borders of major cities, a group which used to be strongly Republican. They also are losing a growing number of college educated voters, and the white working class is getting smaller, so does not offer hope for the Republican party. Geographically, they are practically nonexistent in New England, the Northeast, the Upper Midwest, and California and the Pacific Northwest. They have now lost key battleground states, including Virginia, North Carolina, Florida, Ohio, Nevada, Colorado, and New Mexico, and even in Texas, with the growing numbers of Hispanic residents, the future for the GOP seems gloomy.
The Republicans are becoming more than ever Southern and Appalachian white working class, and culturally conservative and religious devout whites. Even a growing number of women nationally, more than ever before, are voting Democratic.
So the Republicans are being marginalized, and may be in the minority and in the wilderness for a long time, or as Murphy says, entering the "Ice Age",  unless they do major surgery on their party ideology and principles. Maybe they will indeed be replaced by a new major party as time goes by. No one can say for sure, but right now the Democrats are in a commanding position for the long term, as James Carville declared in his recent book.