"I don't have an opinion on every single issue out there. To me, that's, I don't know," Walker answered. "I don't know the answer to that question."
The Wisconsin governor said he supports the current ban that keeps openly gay leaders out of the organization but that he believes the Boy Scouts, not government, should ultimately be able to decide that kind of policy.
Bash and Walker spoke aboard Walker's RV, traveling through Iowa. Earlier in the week Walker told reporters that the Boy Scouts should keep the ban on gay leaders because the policy "protected children."
His campaign later released a statement saying he meant protecting Scouts from the media debate.
"I'm not talking about personal protection. I'm talking about, for me, the reason why I didn't have a problem with it is I just think it pulls Scouting into a whole larger political and cultural debate, as opposed to just saying Scouting is about camping and citizenship and merit badges and service awards, instead of pulling all these other issues out there. And I was just hoping that they could stay focused on that, that's all," said Walker, who is an Eagle Scout.
When pressed about whether that means he is for or against the ban, at first the governor said that's "up to the people who run the places."
Reminded that presidents of the United States are actually honorary presidents of Boy Scouts of America, Walker responded that he would have "plenty much more significant issues to deal with as president."
"From a domestic and foreign policy and national security standpoint, the one thing people find unique, I guess, whether you like it or not, is that I actually answer questions people ask me," Walker added.
With that opening, pressed again, Walker suggested he believes the ban on gay scout leaders is the right policy.
"I thought the policy was just fine. I'm saying when I was in Scouts, it was fine. You're asking what should the policy be going forward. It should be left up to the leaders of the Scouts," said Walker.
On whether being gay is a choice or not, Walker said that's "not even an issue for me to be involved in."
"The bottom line is I'm going to stand up and work hard for every American, without regard of who they are, no matter where they come from, no matter what their background, I'm going to fight for people, whether they vote for me or not," said Walker.
Contrary to popular belief, Walker said, his wife does not disagree with him on same-sex marriage.
In a recent interview with The Washington Post, Tonette Walker talked about how disappointed their two sons were that her husband called last month's Supreme Court ruling legalizing same-sex marriage a "grave mistake."
That story left the impression that Tonette Walker agreed with her sons and disagreed with her husband.
The GOP presidential candidate told CNN that is not the case.
"My wife doesn't disagree with me on my position on marriage. She said she was torn because we have some family members who have some very different views on that. She was torn just because the emotion on the family and because all of the media attention on that. Not because she was torn with me on the position," Walker said.
Tonette Walker's cousin, Shelly, married another woman last month. Alex Walker, Scott and Tonette Walker's youngest son, was a groomsman.
Wisconsin's first lady confirmed to CNN separately that she does, in fact, oppose same-sex marriage, as her husband does.
Last week, GOP presidential candidate Rick Santorum went after the Walkers, saying if she is for same-sex marriage it could have an impact on her husband's policies and positions because "spouses matter."
"He's just wrong," Walker said.