I'm writing this on the 5th of November, with the assumption that the Republican Party loses the 2012 presidential election by almost 70 electoral votes.
That's less of a loss than in 2008, but, of the past six Presidential elections, Republicans have only won once, and "won" another time, and both of those times, the Republican Party received less electoral votes than Democrats did in 1992, 1996, 2008, and 2012. If they want to win a Presidential election, the Republican Party is going to have to stop doing some things, and start doing some others.
Stop acting as the anti-climatology party.
Low-information voters (aka, people who stopped education at or before they graduated high school, and people who only read/watch/listen to partisan 'news') might fall for that whole "global warming isn't real" claim, but that act can't last forever in the 21st century, as warming continues. The Republican Party, if it wants to be taken seriously by intelligent voters, needs to recognize that global warming is real, that it is being pushed by human activity, and that unless countries do things now to mitigate it, it will cost tens-to-hundreds of trillions of dollars more to fix it than if nothing is done to mitigate.
Global warming mitigation is the fiscal conservative position, global warming ignorance is the fiscal stupid position. Evolve.
Speaking of evolution
I understand that teaching good science in schools somehow makes kids less likely to vote Republican, but referring to evolution as wrong is losing you intelligent voters. Grow up. The US needs smart kids in order to become a global leader in science and technology again. Having American-raised bioscientists is going to be easier if school kids don't have to worry that learning about biology will damn them to hell.
Stop being racist
Any Republican Party politician or pundit who mentioned a thing about Barack Obama being "not from America" or in anyway questioned his Americanism because of his skin colour should have been asked to leave the GOP, immediately. America is transitioning from a white-dominated to a white-slight-majority country, probably followed by a transition to a "non-white"-majority country, all potentially in this century. There is no room in the Republican Party for racists, unless it thinks it can win national elections with racist votes (note: not any more).
Oh, and on that note: come up with some form of immigration reform that is more intelligent than "tell Mexicans to leave". There's more undocumented Americans than the population of some states. You can either try to integrate them into society in a calm, respectful manner, or continue losing votes. Your choice.
Stop being sexist
When someone in the Republican Party, usually a older white male, starts going off on female reproductive health, get that guy away from a microphone. Give him an anatomy lesson. If he refuses to learn, ask him to leave the party. The "war on women" meme only works because older white males in the Republican Party think that the reproductive lives of women are under their jurisdiction. That might have been the case in the 1950s, but people (and women are people!) generally do not like it when people they don't know tell them how to lead their lives.
Stop being heterosexist
LGBT Americans are not a major voting block by themselves, but together with their allies, they are a decisive block. Your party is consistently telling these people to vote for a different party. Marriage equality is going to happen in the USA within my lifetime. Get on the right side of history, or continue losing national elections.
Start working against economic inequality
American workers have been at a plateau in pay, at inflation-controlled dollars, since the 1970s. Their bosses have been making more and more over time. This situation will eventually resolve itself, in either a mostly-painless way (raising taxes on the rich and corporations) or in a very-painful way (riots). Work towards the former, not the latter.
In short, be realistic
I know that the Republican Party has to be the opposition party to the Democrats, because the goal of the Republican Party is to win over the voters that find the Democratic Party repellent, and vice versa for them. But over the past two decades, social values are moving away from what the Republican Party is standing for. The reality of global warming is making the economic value of climate inaction less and less reasonable. The Republican Party needs to figure out what is more important: winning national elections, or remaining the party of White 1950s America.