What in your view are the core beliefs of the Republican party in 2008?
Well it's been divided between Nixon wing and Goldwater wing and it hasn't changed. The Nixon wing would include the Bushes and "compassionate conservatism" (sympathy for liberals), and the Goldwater wing would be supply side (influenced by Hayek). Nixon would be Keynesian and pro more intervention in the economy. Goldwater would be more for libertarian economics. Of course if presidents could comeback as ghosts maybe they would change their minds on things. I know that Keynes believed that if he was wrong about unemployment and inflation (which he was during the '70's stagflation) he would go back on his theory. He died before he could see that.
Roughly I would say McCain is aligned to Nixon, and Palin to Goldwater. Both on the ticket seem to be willing to compromise on their differences and push their similarities. They use the classic conservative arguments of Burke which looked at how a democracy can fall apart if government actions aren't for all citizens but for interest groups only. Sometimes voter apathy can occur from this problem. So most conservatives would agree with fighting special interest groups. I don't think they would compromise on that.
More drilling and energy independence is very much what Reagan and Goldwater would want. Conservatives like that. Don't rely on dictators for your energy if you can.
Overturning Roe vs. Wade would definately be a conservative idea. Not just because of abortion but because they don't want the judiciary to legislate from the bench. Let abortion be dealt with by the executive. I believe that McCain is okay with abortion if there is rape, incest, or the mother will die from giving birth. Palin I've heard people say she's against that too and other say she isn't. Go figure. I think most conservatives would be happy with that minimum standard. A few fringe conservatives would want to go all the way but probably can't convince the rest of the republicans on that strict view of abortion. I don't think they will succeed in reversing that because people are becoming more secular over the generations. Religious people can't believe in abortion because they would then have to concede that the mother Mary would have to have the right to abort Jesus. They just can't reconcile that. Abortion is very popular in my country because of its secularness. Conservatives just abandoned it for the current election in Canada.
McCain is more liberal on immigration than many conservatives but it's very popular with the overall public.
In economics cutting spending and removing health insurance barriers between states are conservative and cutting useless spending will be obvious. Most conservatives are not completely libertarian so they will believe in social programs for the needy but they would be focussed on catastrophic situations that people couldn't possibly prevent (acts of god, baby is born with defects, helping mentally ill people, and keeping poor people from starving. Though if they keep adding to the list they are aware that the taxpayer can only take so much before they decide to stop working due to obvious large tax burdens.
The military being supported and an aggressive stance versus the enemies of the U.S. will be a conservative core belief. Endless diplomacy they believe sends a placation signal to bullies.
The military and economic areas are the ones they won't compromise on. The U.S.'s debt burden is in a crisis and I think they have no choice but to fight all the way on it. The U.S. failing to pay their minimum debt payments would be a disaster of Banana Republic proportions. They also don't want to have an attack on U.S. soil while they are in power so they will not cut military.
One thing that is missing (that should be a pushed as a conservative core belief) is the need for savings. We may have in Canada (if the Conservatives win) a savings account where you can put after tax money in and earn investment income tax free. You can invest 5,000 per year and you can take the money out whenever and put back the full amount (5,000 x # of years) back in without any tax penalties. Something like this needs to be pushed so there is an incentive for Americans to save. The entire point of Capitalism is to have an ownership society so people can't be manipulated by social programs and the dependency it creates. Unfortunately it's up to the people to adjust their lifestyles. There's no magic wand. If Americans want to be super consumers and not capitalists they will be weak.
The aging baby boomers will stretch social security leading to cuts in benefits. New Zealand went through that shake up in the '90s. Americans need to save like the Chinese (25% of your paycheck to invest and more if you can). I think the last time Americans saved 20% was in the 80's when there was higher interest rates. After the fall of the berlin wall it was "party time!" all the way until now.
Depending on how the Congress is made up there will be lots of fights. Anybody trying to shake up Washington and the entitlements in there will get a stiff fight a la Mr. Smith goes to Washington. It's like taking drugs away from an addict. I'm sure if they succeed there will be withdrawal symptoms.