The Republican candidates are next scheduled to debate the issues Feb. 25, in Houston, in a contest co-sponsored by CNN and Spanish-speaking TV channel Telemundo. Saturday night's debate in Greenville, South Carolina, featured businessman Donald Trump, Ohio Gov. John Kasich, Texas Sen. Ted Cruz, Florida Sen. Marco Rubio, former Florida Gov. Jeb Bush and retired neurosurgeon Ben Carson.

Unless one or some of the candidates drop out after the South Carolina Republican primary Feb. 20, the same slate of White House hopefuls will likely participate in the Houston debate.

On Saturday night during the CBS News-hosted debate at the Peace Center, CBS News anchor John Dickerson led a moderator group that also included CBS News reporter Major Garrett and Wall Street Journal columnist Kimberley Strassel.

Prior to Saturday's debate, Trump won 34.5 percent of voter support in New Hampshire followed by Kasich with 15.7 percent. Cruz came in third with 11.7 percent followed by Bush with 11 percent. Rubio, who gained ground during the Iowa caucus, came in fifth with 10.5 percent support. With his usual panache, Trump declared after the victory that he would be “the greatest jobs president that God ever created.” 

During his remarks following his second-place finish in New Hampshire, Kasich promised “to re-shine America, to restore the spirit of America and to leave no one behind.”

The South Carolina Republican primary will take place Feb. 20, while the state's Democratic primary will take place Feb. 27. The contests in South Carolina -- as well as Nevada caucuses Feb. 20 (Democrats) and Feb. 23 (Republicans) -- will be important as candidates try and persuade voters before a stream of primaries on Super Tuesday, March 1.