The comments, made on a round of Sunday political talk shows promoting a new book on the topic, come after a week of questions over whether Bush has changed his position on illegal immigration. Bush formerly supported a pathway to citizenship for illegals -- a compromise being debated by a bipartisan group of senators. Now he argues such a pathway would encourage more illegal immigration and shouldn't be a main focus of reform.
Republican senators in the so-called "Gang of Eight" have said they are for creating a citizenship pathway but only after the border is deemed secure enough to fend off a new wave of illegal immigration from those hoping to get in on the deal.
"There is not much light between what we are suggesting in the book and what is being worked on right now, which is very encouraging," Bush said on "Fox News Sunday."
On the larger issue of the Republican party's direction following Mitt Romney's defeat last year, Bush said the GOP must "not just be reacting to what we think is wrong about the president's policies."
"We need to be advocating positive policies as well," he said on "Face the Nation." "And I think there is a growing awareness that that's the case."
Addressing his own political ambitions, Bush -- brother and son of two former U.S. presidents -- said he has not decided whether he will run in the future, and that he won't be deciding any time soon.
"We just had an election. Four years is a long way from now. And I think it's better to stay focused on the things that I'm doing now," he said.
Some in Republican circles questioned whether Bush's assertion he'd consider raising taxes as part of a larger budget deal made such a run impossible. Anti-tax crusader Grover Norquist said of Bush, "People are looking for someone who's tough and you are saying, 'I'll fold.'"
Responding, Bush said, "So, the idea that you have to have this doctrinaire view, you can win a debating point, but you're not necessarily going to be able to solve these pressing problems that we have."