(CNN) -- As major voices within the Republican Party evaluate the GOP's next steps forward, former Florida Gov. Jeb Bush sees promise.

"I'm excited that I think we're seeing the renewal of the conservative movement in the Republican Party and I want to be part of that, for sure," he said in an interview Sunday on CNN's "State of the Union."

What that means for Bush -- the son and brother of former presidents, and thought by some to be a potential 2016 candidate -- and his own political future, however, is less clear.

He has stepped forward as a voice on immigration, releasing a book, "Immigration Wars: Forging an American Solution," that has landed him once again in the political spotlight. Since stepping down as governor in 2007, he also has worked on the issue of education, another issue which he sees as important to his party's future.

"Whether it's the empathy gap or actually having a positive agenda, I would argue an opportunity-society ... agenda is what we need, something that's more aspirational -- a real focus on transformation of our education system, a tax code that doesn't penalize aspiring small business owners, a regulatory system" that doesn't choke small businesses, he said.

He looked at a recent split within the GOP as something "natural" in politics.

Sen. John McCain spoke out strongly against Sen. Rand Paul's filibuster, calling him a "wacko bird." Paul was filibustering to get an answer from the Obama administration on their drone policy and said that while he respected McCain, the respect wasn't always returned.

Bush said, "I would say it is a natural process of where there's divergence, people can express their views openly, but that on the broad issues, there's still broad support and concurrence. The fact that Senator McCain was critical of elements of what Senator Paul said is fair.

"But on the other hand, I think he would respect the fact that Senator Paul got a response from the administration on the key question of whether or not drones could be used against American citizens on American soil," he continued. "And I think it's OK to have a disagreement. We don't march lockstep, 100 percent in agreement all the time."

Bush also played diplomat -- or referee -- when considering President Barack Obama's recent meetings with key Republicans to discuss the federal budget and deficit.

"I don't know what he's doing, but I would encourage him to do more of it," Bush said of the meetings when asked about the president's strategy. "Big issues require everybody to get outside their comfort zone. And people are more willing to do so if they believe that their partner is -- is sincere in their efforts."

He said the recent and upcoming sessions with Republicans in both the House and Senate "could have the chance of restoring a degree of civility. That's the first step to problem-solving and solutions in our nation's capital. ... I think it's important and I applaud the president for doing it."

Are Bush's diplomatic answers a sign he has his sights set on the White House in 2016?

He gave the noncommittal answer many do at this early stage, saying "I don't know if I'm going to run for elected office again or not."

"I've decided to defer any consideration of it until the proper time to make those kinds of considerations, which is out more than a year from now, for sure," he said. "And when I go through that process, I'll let you know. I don't know why there has to be a lot of mystery about this. This is kind of how it normally works, I believe."

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