COLUMBUS, Ohio — With his candidacy surging, Rick Santorum on Saturday questioned the legitimacy of state-run public education systems and suggested that President Obama’s agenda sprang from a “phony theology.”

At one appearance here, he said the idea of schools run by the federal government or by state governments was “anachronistic.” Mr. Santorum did not say public schools were a bad idea, and he said that there was a role for government help in education.

But it was the latest in a series of comments by the former Pennsylvania senator — who is tied in polls in the critical Ohio and Michigan primary contests — suggesting that he takes a dim view of public schooling. He and his wife home-schooled their children.

For the first 150 years, most presidents home-schooled their children at the White House, he said. “Where did they come up that public education and bigger education bureaucracies was the rule in America? Parents educated their children, because it’s their responsibility to educate their children.”