Just because the Republican party lost two Presidential elections does not mean the party is 'doomed'. It has actually fared much worse at points in the past than it right now. At the moment it still controls the US House as well as a majority of Governors and State legislatures. The GOP will come simply come back in future elections.
There are two main parties in the U.S., Democrat and Republican. The Democrat party believes in bigger government, and the Republican party stands for freedom and less government intrusion. There is clearly a place in American politics for the more a conservative and Constitution-loving Republican party. The Democrats have shown themselves to be more and more liberal in policy and thought, and their policies are moving this country quickly toward Socialism. Many Americans oppose this move toward Socialism and are glad to vote for conservative Republican candidates. In fact, many in the House are Republicans. And nearly half of the country voted for the Republican candidate, Mitt Romney. Hence, it is clear that the Republican party still has a place in American politics.
The Republican party should still have a place in U.S. politics because it is important for the US to function under a multiparty system. If there is only a party in the government, there will be a lot of problems, and no one is able to prevent the bad policies from implementation.
A literal interpretation of the constitution at the time it was written is overly simplistic and constraining. It allows little room for growth and ignores the core spirit that the constitution was written with, and that is only one of the problems with the Republican party. They self-righteously condemn members of their own party that don't follow the party line. They are increasingly fundamentalist, and that's a form of extremism that is being rejected more and more often. As the world becomes more connected, everyone's progress will become increasingly interdependent. We cannot afford to do to ourselves what the Republican party is doing to themselves.
Of course we do not want a "one-party" system, we have to have choices. But those choices have to have relevance over a broad population. The Republican Party has embraced some extreme positions that serve to make them seem no longer relevant to a big part of the voting public. So, you could say that they still have a place in US politics but it is a narrowly defined place of their choice. They can continue to occupy that place and offer that narrow choice, but they will probably find that the US public has moved beyond them and they have made themselves irrelevant.