Explaining this is stunningly complicated given all of the variables of the highly intelligent group of Christian Conservatives, but my friends seem to want to know how the pick subverts the "experience" test. Here goes a grossly overly simplistic view that makes some kind of sense to me.
The "Base" believes that:
1) God will raise up whom He chooses to lead (He has a plan for the future and Sarah may be in it).
2) In God all things are possible (even to be President, regardless of what the candidate knows or doesn't know, God will speak to her on the way).
3) Ask and it shall be given to you (the ability to be President).
Here is a true story to illustrate this point.
God was disappointed with a political administration and asked an advisor Samuel to find a new king for Israel. Samuel goes to Jesse's house and asks to meet his sons (the kids with the most experience in domestic and foreign policy). After meeting with the boys, Samuel asks Jesse "Is this all you got?". Jesse replies, "I have the least experienced son out watching the sheep (moose). And Samuel says I'd like to meet him (Sarah).
When Samuel meets him/her God says "this is the one" and Samuel anoints him with oil, sealing the deal, "and the spirit of the Lord came mightily upon him," (NRSV). A kind of magic from God happens to David to give him what he needs to be King.
The kid (David) goes on to work in the palace under the much older King Saul and eventually becomes the greatest King of Israel. Sarah is however not David and needs a few more Lyre lessons but seems to be an eager student. Saul here is sounding like McCain.
There may be a sense in some of the "Base" minds that Sarah is part of God's plan here, like the story, and that works for McCain. McCain's advisors are betting on their gullibility. How did this unknown get picked? It must be God's plan. There must be a miracle in the works. Roe will be overturned, Islam will be converted, and the USA will be returned to a Christian Nation.
This may be the dream of some of the base but this is not God's way and McCain's advisors will be bitterly disappointed in the end. I believe this is what they were looking for when Sarah was picked. Magic is not really God's plan and most of the base knows this.
The idea that there is magic (I think a kind of idolatry) that will turn the election or is manifesting in Sarah is dangerous to the Base and McCain. I think the advisors are hoping there are a number of people who believe in magic which will turn into votes. Compassion and service are God's path and miracles are made through inspiration not desire. The base understands this.
Don't trust the advisors. Times have changed in the last 8 to 30 years. Hopefully the allure of magic has worn off. The Christian Right are smart and have learned a lot. What if they want a peacemaker (Obama) rather than a warrior (McCain)? While the Base may like some of the positions of Sarah they may still be put off by the divisive aggressive approach of the top of the ticket. Oh and there is also her inexperience in all things National.
The story may illustrate the logic of the political advisers however it may not stick with the contemporary Base.
A few may believe in magic but I hope most believe in the Lord.