The key to understanding the "abuse" of the Christian Right by the political leaders is singlefold.
If one were to say that abortion is murder of a human (and the Church itself didn't make this into an issue until 1850(need link 1)), then people who support abortion are unapologetic killers of 40,000,000 people. These numbers place Democrats, in the eyes of these zealots, with Hitler, Stalin and Mao.
Yes, the Christian Right are a bunch of ignorant rubes, but they might be seen, by false comparison, as anti-slavery voters. Did you know that the early Republican Party, under Lincoln, Grant and Ames(House Leader), were some of the most corrupt office-holders in US history? Lincoln had spent over 20 years as a lawyer for the railroad industry(link 2). Grant's scandals are legendary(3). Under Oakes Ames(4), a rich railroad magnet could buy Congressman to get the rights to buy the land to build their iron horse track across the country.
But the people couldn't vote against them, because the alternative was slavery and the Civil War. For fifty years, from James Buchanan until Woodrow Wilson, no Democrat became President except the honorable Stephen Grover Cleveland(link 5).
Sadly, it seems we are in the same position today.