(CNN)After stumbling this week, Jeb Bush heads into Thursday's debate facing a key question: Is he ready to run for president in an era when every gaffe can go viral?

Bush's latest challenge came Tuesday when the former Florida governor attempted to slam Planned Parenthood. But he appeared to veer off track when he said, "I'm not sure we need half a billion dollars for women's health issues," referring to the amount of money the federal government pays largely for low-income women's health services.

Bush later said he "misspoke," but the line gave an easy opening to Democratic presidential front-runner Hillary Clinton, who immediately pounced to portray him as insensitive to the needs of women.

The fumble followed an uncomfortable moment Monday at a forum in New Hampshire when Bush struggled to answer a question about his family's political legacy -- an issue that has repeatedly tripped him up during his campaign.

Bush allies argue that these moments amount to blips that will soon be forgotten and say that by staying the course, he's showing an even-handed steadiness that could help him secure the nomination.

Still, the incidents underscore how Bush, the powerhouse politician who was once thought to be the man who could clear the GOP presidential field, is struggling to find his footing in a race that's been upended by Donald Trump's surge in the polls.

Perhaps more importantly, the missteps raise questions about whether Bush is ready to wage the type of disciplined, savvy campaign required in the modern political era to win the White House.

"It speaks to the changes in campaigns since the last time he ran for office. It used to be you make a comment like that; by evening you put out your statement, and the statement ends up in the same story. That whole thing on women's health issues swept around the world before the campaign retracted it," said Katie Packer, a former adviser to Mitt Romney who specializes in helping candidates hone their message to Republican and independent women. "The speed at which things travel is probably new to him. You learn that when you're running, especially in the presidential cycle. All of this serves to make him look a little out of touch."

Packer is neutral in the race but she is founding partner of WWP Strategies, which works for GOP presidential candidate Marco Rubio in Michigan.

When a candidate stumbles the first time, as Bush did earlier this year when pressed on his brother's invasion of Iraq, Packer said, some voters gauging his electability might have given him a pass -- thinking he simply wasn't prepared for that particular question. "But if they keep not getting these answers sharp; it starts to look like you're just not sharp" as a candidate, she said.

While Packer said Bush won't ever be able to "totally clean that (Planned Parenthood comment) up, he's going to have to come out very strongly in advocating what his position is on women's health and what the federal government's role is in that."

Candidate appears to take the long view

Some of the candidate's close allies are concerned that he has a tendency to come off as dismissive, particularly in group forums where he doesn't like the question. They hope he can keep that sort of demeanor in check, as it generally does not go over well with voters. On the policy front, he has been preparing intensively for weeks -- working to get his complex policy positions boiled down into 30 second and 60 second bites.

Still, many allies said he's simply playing the long game.

"Presidential politics isn't very different from professional football -- quarterbacks are going to throw interceptions, and sometimes those interceptions might fall at the feet of the quarterback. And Jeb Bush just threw one," said Steve Schmidt, a Republican strategist who advised George W. Bush and John McCain. "He has to understand the demographic challenges facing the Republican Party and little things like that make it difficult to win the game."

"That being said, the proportionality of the reporting on this issue is completely overblown," Schmidt added.

Bush has done all the right things, advisers said, by standing up to his critics on difficult issues such as immigration and the Common Core education standards and paying attention to the arcane but vital elements of a winning campaign -- such as ensuring ballot access.

Bush has made countless phone calls to activists and influencers in Iowa, New Hampshire, South Carolina, and Nevada — while simultaneously building his support slowly and steadily with a tireless campaign schedule. And then there's his treasury: the fact that he stockpiled more than $100 million through his campaign and pro-Bush political action committees that will allow him to stay in the race long after other candidates run out of money.

Ultimately, he's embracing his image as the boring candidate and eschewing the theatrics of his fellow Republicans, who have done everything from taking a chainsaw to the tax code to putting their cell phone in a blender to get attention.

Longtime Bush-watchers such as Susan MacManus, political science professor at the University of South Florida, said the former Florida governor should not be underestimated.

"He is not a 'for-the-moment' person; he is more calculating and always looking long term," MacManus said. "He is trying to be the statesman and anticipating that Trump will wear thin. He's just really trying to stay the course right now, which compared to the others, he's doing pretty well with."

A strategy of staying the course

Voters "are not really honed in right now and making decisions," MacManus said. "People in Florida," for example, "don't care a whit about politics right now."

Because of that, many longtime political observers say there is an advantage for Bush, and other strong candidates such as Wisconsin Gov. Scott Walker.

Veteran strategist Charlie Black said Bush's position is a comfortable place to be right now because "the race hasn't really started. It starts with these debates."

For all of Bush's discipline and his mastery of the issues, he has yet to show he can channel the seething anger among Republicans like Trump.

But from Bush's perspective, "if you look at infrastructure, organization and money -- he's the front-runner. And he's got a lot of appeal as people get to know him," which is the opportunity that the debates could offer, Black said.

"I think he's the best campaigner in the family; he's completely knowledgeable about policy and he can answer questions without hesitation, and personality-wise, he's just a little more engaging and smooth than his brother or his father.

By contrast, Black predicted that the debates will be the arena where Trump begins to fade "as voters learn more about his positions and lack thereof."

"My guess is that Trump will play it straight here, abide by the rules, but he'll still be bombastic and not get into details," Black said, "and if he does that for four straight debates, by then, people will figure him out."

For Bush, the onus Thursday night will be to show voters that he is the calm, steady hand -- the one, as Hillary Clinton might put it, who you wanted answering the phone at 3 a.m. in the middle of a world crisis.

Longtime Democratic strategist Bill Carrick said even with all the anger festering in the Republican Party right now, that group of voters is not quite big enough to ensure victory. The quieter, more statesman-like candidates are ultimately due for a serious look from voters, he said.

"In these multi-candidate debates early on, there is something to be said for staying out of traffic: because, you know, a lot of accidents happen in traffic," Carrick said.

The silver lining for more understated candidates such as Bush, Carrick said, is that Trump's presence will ensure a blockbuster audience for this week's debates -- including the independents and moderate Democrats that Bush would like to appeal to in order to ensure his path to the nomination.

While Trump may entertain, Carrick said: "There is a point at which people start looking for a president. And Republicans want to win."