About a month ago, my battery decided that it had had enough of Phoenix and Austin summers. When it went dead, the power to my car's electrical system was completely lost. When I got a new battery and started my car, my stereo prompted me to input some sort of anti-theft code. I screwed around with it sufficiently that it eventually locked me out entirely. Now I have no car stereo. That means that when I drive around, there's really nothing for me to do but: a) drive, and b) think. In the course of doing the latter, I solved all of the GOP's current problems...or at least I made them much easier to solve. Watch now, as I reveal the whole thing in the space of one short paragraph.
The GOP needs an agenda. Republicans on the national level will never support a tax increase, and they should support a balanced budget, so they know how much money they have available to support their agenda--however much money the government brings in every year. They also know that part of that money has to go to national defense and debt service. They can use whatever is left to fund the rest of their agenda. How do they figure out what the rest of their agenda is? The same way they figured out the first two items (national defense and debt service): by asking what things are absolutely critical for the health and survival of the country, and what things can only be done properly at the federal level. Once they identify the items in the overlapping areas of those two circles, they can say, "These things get first dibs on our revenues. If we have money left over after paying for them, we can talk about some other stuff. If we don't have enough money to pay for the things that get first dibs, then either: a) we'll have to scale back our ambitions for some of them; or b) we'll have to raise taxes." If individual Republicans find it more distasteful to raise taxes than to scale back their ambitions on their mission-critical issues, then that's a choice they can make. Presumably, that's the choice that an overwhelming majority would make (would make, that is, if they were genuinely committed to a balanced budget; if they were not committed to a balanced budget, they'd just keep borrowing money).
So, that was the explanatory paragraph. Let me give you a highly simplified example. Let's say that we've got $100 in federal revenues. Republicans say, "Okay, that's what we have to spend. To service our debt and to fund our national defense to the level that we think is appropriate, we'll have to spend $30. That leaves $70 to pay for everything else. So, what are the other critical things that the federal government needs to do, and that only the federal government can do properly? Probably: 1) make sure that everybody has health care, through either public or private sources; 2) make sure that every kid and every adult has access to an education that will allow him or her to be self-sufficient; 3) make sure that old people are taken care of through either public or private sources; 4) seal our southern border; and 5) start paying down our national debt. All of that will cost $60. That leaves $10 to fund the operations of government, put away for a rainy day, etc."
Okay, now a few points. Whatever agenda the GOP comes up with (which will almost certainly not be the one I came up with as an example), someone will say, "But what about THIS? You haven't allocated any money to it." A good "this" from my example would be basic welfare programs for the poor--cash assistance, food assistance, wage subsidies, child care and transportation subsidies, etc. I haven't set aside money for any of that. But the leverage in this exercise comes from two things: 1) you know you want to balance the budget; and 2) you start building your agenda based on the amount of money you have, not on all of the perceived needs out there. That way, whenever someone says, "But what about X?", you can say, "We don't have enough money for X. So, if you want X, either we're going to have to raise taxes in order to keep the budget balanced, or we're going to have to get rid of Y. As Republicans, though, we're not prepared to raise taxes, and we think Y is more important than X. If you disagree with us, you can vote for the Democrats."
See what I'm getting at? It's a world of nearly infinite problems, but of finite resources. If the GOP wants to balance the budget, then they've got a much smaller pot of money to play with than they've been playing with for the last 30 years or so. That pot of money can only fund a handful of the most important large-scale federal undertakings. That makes the job of constructing a Republican policy agenda pretty easy.
So, Republicans, pick your handful of issues, make the case for those issues being the top three or four or five out there, present your center-right solutions to them, tell people that these issue solutions are necessities that have to be paid for before we can start paying for luxuries, and tell people who want more than your handful of solutions that what they're saying, in effect, is that they want to raise taxes or continue borrowing from future generations, neither of which the GOP is prepared to support. And if you lose following this approach, you lose--that means either that you picked the wrong issues, politically speaking, which is something that can be remedied, or that the public doesn't support a basically conservative federal policy agenda, so there's not much point in there being a national Republican party anyway.