WASHINGTON (CNN) -- Scott Walker -- the Wisconsin governor who built a political brand around bold actions -- is increasingly playing it safe as he eyes a White House bid next year.

Walker is under fire for failing to disown comments from Rudy Giuliani in which the former New York mayor said he doesn't believe President Barack Obama \"loves America.\"

\"He doesn't love you. And he doesn't love me,\" Giuliani said at a dinner that Walker attended this week, according to Politico. \"He wasn't brought up the way you were brought up and I was brought up through love of this country.\"

When asked about the comments during a CNBC interview, Walker refused to rebuke Giuliani.

\"The mayor can speak for himself,\" Walker said. \"I'm not going to comment on whether, what the president thinks or not. He can speak for himself. I'll tell you I love America, and I think there are plenty of people Democrat, Republican, independent and everybody in between who love this country.\"

The deflection comes after Walker, during a visit to London last week, punted when asked if he accepted the idea of evolution. \"That's a question a politician shouldn't be involved in one way or the other, so I'm gonna leave that up to you,\" Walker responded.

He later released a statement seeking to clarify his views. \"I believe faith and science are compatible, and go hand in hand,\" he said.

If politics is a circus, then running for president is the high-wire act. And while one high-profile stumble could derail a campaign, there also might be a risk in playing it too safe.

The refusal to fully engage on the question about evolution or to pass some kind of judgment on Giuliani's comments creates a dissonance with Walker's would-be campaign message: that he represents \"fresh leadership\" and is someone with \"big, bold ideas and the courage to act on it.\"

While his handling of the two episodes might not cause him much pain with the Republican base, it could pose problems down the road in a general election with independent voters. On the question of evolution, specifically, 65 percent of independents believe humans evolved over time, according to a 2013 Pew Research Center survey.

For Walker, who is still introducing himself to voters around the country, he must make a calculation when it makes sense to lean in, and when to play it safe.

\"Whenever you run for president you are playing a high-stakes game of poker,\" said veteran GOP strategist John Brabender, who advised former Pennsylvania Sen. Rick Santorum's 2012 presidential campaign.

\"There is so much risk in saying the wrong thing, you will find in the short-term people who will be cautious,\" he added. \"Great campaigns know there is a time to run and a time to walk.\"

The time for running will come soon enough, with candidates likely to launch their official bids in the coming months, and primary debates soon to follow beginning in August.

In the meantime, Brabender expects the 2016 contenders will focus not just on building up their name identification with voters, but their \"brand equity,\" which could help to blunt a misstep once the campaign is fully joined. Consider it the lesson of former Texas Gov. Rick Perry from 2012, whose prospects failed to recover from his infamous debate lapse.

\"Because there are so many qualified candidates, one mistake can be too many in a race like this,\" Brabender said. \"You don't get multiple opportunities to introduce yourself.\"