Matt Rourke/AP Photo

Former Florida governor Jeb Bush today suggested that the chances of a Republican controlled House of Representatives defunding Obamacare are slim, but the risks are high to the Republican Party if they fail to fund the government.

"If you control one half of one third of the levers in Washington, D.C your ability to influence things are also relative to the fact that you have one half of one third of the government," Bush said at the National Press Club today. "That's the reality."

Bush, who has frequently offered advice to the G.O.P that has strayed from the more conservative base of the party, added that as the country approached the real deadline for when the government runs out of money to fund its operations, the stakes would get higher for Republicans.

"This isn't a hypothetical," Bush said. "So as we get closer to these deadlines there needs to be an understanding of that or politically it's quite dicey for the Republican Party."

Bush's statements are in sharp contrast to Louisiana Governor and Chairman of the Republican Governors Association, Bobby Jindal, who said the effort to "repeal and defund is certainly a fight worth having."

"I don't know why as a party we would ever try to negotiate with ourselves for taking the option off the table," Jindal said. "It's certainly presumptuous for us to think that the president will choose to shut down the government over this."

The split between the two men is emblematic of a divide in the GOP. Establishment Republicans like Bush believe a push to defund Obamacare this fall is doomed to failure, and could potentially imperil the party. Others, backed by strong Tea Party pressure, believe this is the only opportunity Republicans have to oppose the law before some parts go into effect on Oct. 1.

Both men agreed, however, that Republicans need to have an alternative to Obamacare, rather than simply pushing to defund the law.

"I don't think they have the ability to implement it effectively," Bush said. "So this debate will go on, because it's not going to work and when it's not going to work, to the governor's point, Republicans better have a clear, easy to understand alternative that is based on some guiding principles that we know will work because our country really needs a completely different health care system than what we have today."