http://en.wikipedia.org/wiki/Rockefeller_RepublicanRockefeller Republican refers to a faction of the United States Republican Party who held moderate to liberal views similar to those of Nelson Rockefeller. The term largely fell out of use by the end of the twentieth century, and has been replaced by the terms "moderate Republican," "liberal Republican", and the derogatory term RINO. Modern Rockefeller Republicans are sometimes socially conservative and more fiscally centrist, while others are fiscally conservative and socially liberal. Still others espouse government investments in environmentalism, infrastructure, farms and higher education as necessities for the nation's survival, in the tradition of Alexander Hamilton and Theodore Roosevelt. In general, Rockefeller Republicans oppose socialism and the redistribution of wealth while supporting some regulation of business in matters pertaining to the public good. Richard Nixon, often considered the last Rockefeller Republican president, founded the Environmental Protection Agency, cooled relations with China and the Soviet Union, and referred to himself as a Keynesian.
Although there is at least one blog purporting to be "Eisenhower Republican":
http://ikeonic.blogspot.com/2010/04/ten-principles-of-eisenhower-republican.html1) We remain loyal Republicans, in good times and bad.
2) Government is not the problem, but government can't solve every problem.
3) Government has a duty to develop infrastructure per the Commerce Clause.
4) Government should empower consumers with “Goldilocks” regulation of free, fair marketplaces.
5) The government should not reward laziness and guarantee you a free ride through life.
6) Government should act to conserve, manage and protect vital, finite resources.
7) Roe v. Wade and decisions like it are a terrible rewriting of the Constitution.
8) Every dollar in increased taxation decreases economic freedom.
9) When we go to war, we go all out or we don't go at all.
10) Americans must do what we can to promote and preserve freedom around the world.
(At the actual site each of those comes with explanatory text)
About seven of those (maybe 6 1/2) would fit Democrats too, but some of those are also either "stealth" positions on other issues, or just ignoring how some of those play out in reality.