Rick Santorum is sticking by earlier questions he posed about former rival Mitt Romney's authenticity, saying the points he made during the primary campaign were legitimate.

Santorum said Sunday "I don't back away from any of those things."

Santorum had also argued in March that Republicans should give President Barack Obama a second term because Romney wasn't conservative enough. The former Pennsylvania senator now says "clearly, the difference between President Obama and Mitt Romney is a chasm."

Should Romney win in November, Santorum says he would advise Romney if asked but not serve in his administration. He said: "It's pretty much a flat no."

Santorum tells CNN'S "State of the Union" that he wouldn't consider working for a Romney administration because his priority lies with his family.