This is more of a jot list than a well thought-out proposal. Here are three (serious) ideas for how the Republicans--especially those in the House--could actually govern better and regain some political credibility for their brand. From most to least plausible:
1) Work with the president on immigration reform. Seriously, this is a no-brainer. Our system provides no legal means of migration for unskilled workers, a byzantine, slow, and expensive process for permanent residency even in the "easy" categories (trust me on this one), and cruelly punishes children for their parents' choices. Specifics could be tough to hammer out, but a robust guest worker program and something resembling the DREAM Act (though I am not a fan of the college/military requirement) would be a damn good start.
And there is that elusive Hispanic vote. Putting a Cuban guy at the top of the ticket isn't going to solve that for you.
2) Work with the president on entitlement reform. Again, the specifics could be tough, but we already have a perfectly tenable starting point: the Bowles Simpson commission's recommendations. We don't have to scrap Social Security and start over: raise the retirement age, raise the cap on income subject to SS taxes (this hasn't happened in a long time, making it the most regressive federal tax), and means-test benefits. That is the very definition of a conservative (in the original sense of the word) reform.
3) Repeal DOMA. Hear me out on this one. The only thing left for those of you opposed to marriage equality is to fight a war of attrition for as long as you can. The rest of us--not to put too fine a point on it--will outlive you.
I often hear from my friends on the right that they aren't opposed to gay people per se so much as having a change forced upon them by the courts. Well, here's the thing: there are now states that have approved equality through your allegedly preferred channels. (And there are others that while regardless of how they got there, have it.) There will be more. And eventually someone is going to sue for federal recognition of their marriage and/or full faith and credit recognition among the states. This will happen. It will go to the Supreme Court. And eventually, they will win.
If, however, DOMA is repealed, then you pave the way for federal recognition via a legislative process. You leave open the possibility that states may decide to recognize same-sex marriages from other states without having to license them themselves. Most importantly, you head off the contentious Supreme Court decision that you (rightly) worry will leave the country divided and a substantial minority feeling completely disenfranchised.