President Donald Trump, faced with the failure of the Senate Republican health care bill, says Obamacare will fail, and he'll make sure he's not taking the blame.

"We're not going to own it. I'm not going to own it," Trump said Tuesday at the White House in his first public appearance since the Senate bill fell apart. "I can tell you the Republicans are not going to own it. We'll let Obamacare fail and then the Democrats are going to come to us."

All presidents point fingers at the opposing party. But Trump's attempt to pass the buck on his party's failure to approve a health care reform bill breaks with the way his predecessors sought to tout the power of the presidency by arguing responsibility stops in the Oval Office -- and could contribute to his difficulties facing his administration during its first six months and beyond.

Trump's comments track with his governing style. Vice President Mike Pence, top White House aides and Health and Human Services Department leaders were taking point in negotiating with Congress, while Trump made phone calls and held meetings with individual or small groups of lawmakers. But Hill Republicans say Trump didn't use his bully pulpit to sell the health care bill, and when he did, his comments were in general terms about improving health care, despite the complexities involved in the legislation.

"He was playing with a firetruck and trying on a cowboy hat as the bill was collapsing and he had no clue," a top Republican told CNN on Tuesday, mocking the President's "Made in America" week events at the White House on Monday.

Trump's aides have been happy to play up the President's interactions with Republican senators -- he made calls from France last week and over the weekend from New Jersey, officials told CNN. And he was dining with GOP senators Monday night when the bill collapsed. But because of his disengaged style, Trump has made a habit of complicating the negotiating process by saying things that contradict previous positions or statements.

Case in point: While meeting with Republican senators at the White House in June, Trump said the House-passed health care reform bill he celebrated earlier this year was "mean," according to a source in the room. The comment belied the celebratory Rose Garden ceremony Trump hosted when the House passed the bill and the President championed it as "incredibly well-crafted."

But as the bill failed, Trump and his White House are pointing to the Democrats, despite the Senate being controlled by Republicans. Their argument: Obamacare's problems are the Democrats' to own, even if GOP efforts to repeal it go nowhere.

"Look, I think we are taking responsibility in terms of pushing new legislation through but not the failures of legislation that happened before the president got into office," said White House deputy press secretary Sarah Huckabee Sanders. "I think you also have to take into account the outrageous obstruction that we have talked about pretty frequently up here, not just on health care, but across the board."

Trump, however, wasn't happy when President Barack Obama would point fingers at Republicans for blocking his legislative agenda.

"Obama's complaints about Republicans stopping his agenda are BS since he had full control for two years," Trump tweeted in 2012. "He can never take responsibility."

Obama's complaints about Republicans stopping his agenda are BS since he had full control for two years. He can never take responsibility. — Donald J. Trump (@realDonaldTrump) September 26, 2012

The concern for Republicans is that Trump's style on health care -- and the bill's possible failure -- will carry over to efforts to pass sweeping tax reform.

"There is only one dynamic that is different from this year and past GOP struggles to repeal Obamacare and that is President Donald Trump," said Doug Heye, a former communications director at the Republican National Committee. "Throughout this process, he has essentially stayed on the sidelines, instead of using his enormous influence with his base to push the bill forward and increase its popularity."

JUST WATCHED Borger on Trump: This isn't leadership Replay More Videos ... MUST WATCH Borger on Trump: This isn't leadership 01:22

He added: "The finger-pointing is predictable, but also hurts the chances of future legislative victories Republicans need for a motivated base in the 2018 elections. Republican margins of error are slim and all hands, especially from the White House, need to be on deck."

The comparisons to past presidents is striking

Truman had a small, walnut wood sign on his desk with the phrase "The Buck Stops Here." The sign, according to the Harry S. Truman Library & Museum, was made in the Federal Reformatory at El Reno, Oklahoma and given to him by Fred Canfil, a friend and the United States Marshal for the Western District of Missouri.

"You know, it's easy for the Monday morning quarterback to say what the coach should have done, after the game is over," he said in 1952. "But when the decision is up before you -- and on my desk I have a motto which says The Buck Stops Here' -- the decision has to be made."

And during his farewell address, Truman specifically implored his successors to take responsibility for the decisions they make in office.

"The President -- whoever he is -- has to decide," he said. "He can't pass the buck to anybody. No one else can do the deciding for him. That's his job."

More recent presidents have adopted Truman's phrase -- even if they, at times, have also passed the buck.

"The buck stops with me," Obama said after intelligence failures led to an unsuccessful Christmas Day bombing plot in 2010.

And in 2009, as his administration came under fire for allowing executives at failed insurance company AIG to leave with bonuses, Obama channeled Truman.

"Ultimately I'm responsible. I'm the President of the United States," he said, adding later, "The buck stops with me. And my goal is to make sure that we never put ourselves in this kind of position again."

President George W. Bush, too, wasn't known for taking the fall, but he did take responsibility after Hurricane Katrina devastate the Gulf Coast and left over 1,800 people dead.

"Katrina exposed serious problems in our response capability at all levels of government and to the extent the federal government didn't fully do its job right, I take responsibility," he said.

The same was true for Bill Clinton, who certainly passed the buck at times, but also acknowledged in 1998 that he "misled people" on his relationship with Monica Lewinsky.

"I know that my public comments and my silence about this matter gave a false impression. I misled people, including even my wife. I deeply regret that," he said.

President Jimmy Carter even borrowed the original Truman sign, displaying it on his Oval Office desk during an address to the nation on energy in 1979.

Trump's comments aren't just breaking with his predecessors, either. He is breaking with himself.

"Entrepreneurs: Everything starts with you. Realize that you're in charge. Whatever happens, you're responsible," Trump tweeted in 2015.