COLLEGE STATION, Tex. — With eyes increasingly on him, Jeb Bush signaled on Sunday the kind of campaign he would mount if he runs for president, one arguing against ideological purity tests while challenging party orthodoxy on issues like immigration and education.

Even as he sharply criticized President Obama for his handling of foreign affairs and health care, Mr. Bush made clear that he would run against the style of politics that has characterized recent Republican nominating contests. He said he would decide by the end of the year, in part on whether he thinks he could avoid “the vortex of a mud fight” with a “hopeful” message.

“We need to elect candidates that have a vision that is bigger and broader, and candidates that are organized around winning the election, not making a point,” Mr. Bush told an audience at the George Bush Presidential Library and Museum. “Campaigns ought to be about listening and learning and getting better. I do think we’ve lost our way.” He added, “I’m not being critical of my party, but campaigns themselves are reflective of this new America.”

In perhaps his most expansive public discussion yet of a possible candidacy, Mr. Bush, a longtime supporter of overhauling immigration laws, warned against “harsh political rhetoric” on the subject and urged more compassion for those who enter the country illegally for economic reasons. “Yes, they broke the law, but it’s not a felony; it’s an act of love,” he said. “It’s a different kind of crime. There should be a price paid. It shouldn’t rile people up that people are actually coming to provide for their families.”