This post is in response to Susan's request.
Christians come in all shapes and sizes. They have different levels of spiritual insight and application. They also have tendency to see their particular point of view as the "correct one". One distinguishing characteristic is something called "the Christian World View" (CWV). The CWV is the idea that Christians should have a unique theologically informed philosophy that governs how they see the world.
The CWV runs the spectrum from people who call themselves Christians but whose personal philosophy is identical with the cultural around them (Worldly World View i.e. WWV), to Christians who have a highly developed sense of how Hashem sees the world (Highly Christian World View, HCWV).
Of the three types of Christians (WWV, CWV, HCWV) the CWV group can be further divided into those who recognize or are Aware of a CWV (ACWV) and those who have a CWV but are consciously Unaware of their CWV (UCWV).
Folks who tend to be involved in what Susan is identifying as "dominion theology" tend to have a CWV and also tend to be very aware of that view ACWV and have a desire to act on it in a political forum. Being ACWV and politically active is not new. The first modern example that popped into my mind was the Moral Majority movement that Jerry Falwell started up in 1979.
In the United States CWV has been linked with political philosophy since before the beginning of the country. The first amendment to the constitution of the United States was widely understood as a declaration to practice the Christian religion without fear of a state sponsored church. The founders were very much ACWV and willing to incorporate it into their political philosophy. This ideological phenomenon was a direct consequence of the First Great Awakening 1730 to 1740.
Regardless of the CWV of the founders, the populace of the United States increasing followed a secular personal philosophy. The public institutions in the United States, such as the courts and the public schools, still maintained the tenets of the Christian religion. School children were taught that morality, character etc were based on the Bible. Judges still used scriptural principles in their findings. The upper classes of American society held to a firm belief in the basic Christian tenets as commonly taught. The result was that when the nations clergy looked around and saw the falling state of public morality, and preached against it America enjoyed the Second Great awakening 1820-1850.
One idea that became increasingly common in both religious circles and in political environments was that of manifest destiny. Also very common in the minds of America Christians in the 19th centaury was the theological belief that Christians could and should make heaven on earth. This doctrine is sometimes identified with the eschatological position of Postmillennialism. The post millennialist paradise was the goal of most of the ACWV crowd from 1800 to the 1930's.
For examples major trends in American Cultural Topics:
The first tax-supported public school was run by Rev. Ralph Wheelock.
As a sub-issue / proof examine the laws requiring slave owners to educate their slaves to read so that they could understand scripture and reject their heathen religions.
Modern Welfare State
Has roots in the policy beliefs of Christian Socialists of the 1920's and 30's.
Faith Based Initiative
Involves using Christian Social Justice organizations to execute government policy programs. For example: Refugee resettlement programs.
The seven examples cited above all share the common link of making the United States into a Christian paradise. Third Great Awakening 1880-1930 laid the groundwork for the modern Poltical Dominion Theologists (PDT).
The modern American PDT tends to be ACWV and aware of the American history and the role of Christian Political Activism. In the past, the gains in America's economic, cultural and political followed, i.e. came after, the periods of spiritual revival. In my estimation todays PDT wants to create a spiritual revival by using political power as a means to that end.
I see Donald Trump as a person who claims Christianity but has acted as if he had a WWV for his adult life. He may be moving towards a CWV at this time. If that is the case he is probably UCWV. He seems to want to restore the basic institutions of a historically great America by focusing on the political and cultural institutions that have been corrupted and broken. He believes that he can do that because he understands the fundamental flaws in the decision making process that have brought us to where we are today. That may seem egotistical, but I believe it is an accurate estimation. He doesn't wave a Christian Battle flag around, because he doesn't see the political as a reflection of the spiritual.
I have no idea what Cruz believes. I don't think anyone else does either. Most of his association is because of his dad's remarks, not his. Based on his dad, Cruz is probably ACWV. How highly developed that is, I can't say. Being ACWV gives him the ability to see and tell others about issues that are important to people with CWV. Communication along those lines seems to be popular with others who are CWV. Ted Cruz is willing to wave that flag if it rallies supporters to his campaign.
Personally, as a ACWV person, I believe that America must follow the same path today as it has in the past. The spiritual revival must take place first. Then we might see some worldly benefits. Ted Cruz isn't interested in doing that, so I can't take his version of occupying the Whitehouse as some form of Spiritual Manifest Destiny. I don't see Trump as that guy either, but he's not trying to tell people that he is.
Hope that helps Susan.