President Donald Trump is in the position of not only changing his White House chief of staff but also changing the subject – and maybe changing his tactics, too.

The Republican drive, seven years in the making, to overturn and replace the Obamacare health-care plan crashed in failure late last week, providing the U.S. President with a sobering lesson in the limits to his power. One of the signature elements of the Trump presidency and a surefire applause winner at Republican political rallies through three U.S. congressional election cycles, the Obamacare repeal effort simply petered out. This prompted the Trump administration to say Sunday that it would decide this week whether to cut off the payments Washington makes to insurers to keep the costs of health-care policies low.

The GOP's failure to overturn Obamacare almost certainly signals the end of the Republicans' belief that they can govern without providing a voice, or forum, to their Democratic rivals.

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Read more: Reince Priebus departure caps a week of turmoil for Trump

Read more: What just happened with the Obamacare repeal? A guide to this week in the Senate and what's next

More broadly, that failure – "a historic debacle," in the characterization of the conservative editorialists of The Wall Street Journal, "that will echo politically for years"– has vital implications for the U.S. economy and for the country's political profile.

It means, to be sure, that Obama-era regulations requiring most Americans to have health insurance remain in force, along with strictures governing patients with pre-existing health conditions – as well as some of the financial problems that even Democrats acknowledge must be addressed.

But it also means that there is less flexibility for Mr. Trump and his Republican allies to manoeuvre on his next priority, overhauling the American tax system. And it underscores the difficulty the maverick President is having in navigating the buoys of political Washington.

Moreover, the failure of the Obamacare repeal – the President said in a weekend tweet that his putative Republican allies looked "like fools" and worried that Republican senators might be "total quitters" – underscored the difficulties ahead for simplifying the tax system and reducing some taxes, especially corporate taxes.

Even with a retired Marine Corps general, John Kelly, newly installed as Mr. Trump's chief of staff, the White House is coming to terms with how resilient and resistant are Washington's other power centres. In short, the "swamp," as Mr. Trump often calls Washington, retains its power.

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Aligned against Mr. Trump in the health-care episode were more than his Democratic rivals, who provided a formidable united front and who contributed not a single vote for any of the myriad proposals to replace or repair Obamacare. Also against him were moderate Republicans, devoutly conservative Republicans and an array of other forces, including powerful hospital and health-insurance trade groups.

In the next battle, tax overhaul, the same phalanx of opponents will line up against Mr. Trump, but this time they will be energized by their triumph on health care. They will be joined by scores of other lobby, trade and think-tank groups, all of whom are experienced veterans of the Washington power game. The departure of Reince Priebus, the ousted White House chief of staff who had been the chairman of the Republican Party and a veteran capital operator, may only increase the President's isolation from establishment Washington and heighten his vulnerability to the political tricks they have mastered over many decades.

Mr. Trump and Senate Majority Leader Mitch McConnell of Kentucky almost certainly learned one important lesson from the health-care debacle: Even a rebel President has to follow the legislative rules in Washington. With Mr. Trump's support, Mr. McConnell crafted his principal piece of legislation with a small group of lawmakers who met in secret. There were no hearings, which are one of the staples of Capitol Hill life. Nor, until the end, were the viewpoints of likely dissenters aired – or ameliorated.

One Republican senator, Lindsey Graham of South Carolina, was so disgusted that he said he hoped the House would vote down the very bill he voted for. Others felt that way privately. The American Conservative Union assailed what it called "GOP sellouts." The handful of moderate Republicans came away empowered. And at the end, lawmakers seemed determined, or at least resigned, to return to the traditional way of shaping legislation.

"We've tried to do this by coming up with a proposal behind closed doors in consultation with the administration, then springing it on skeptical members, trying to convince them it's better than nothing, asking us to swallow our doubts and force it past a unified opposition," cancer-stricken GOP Senator John McCain of Arizona said. Mr. McCain left a hospital bed to join the health-care debate only to provide the vote that doomed the Republican effort to repeal Obamacare.

With the North Korea nuclear crisis mounting in the background and with conservatives troubled by the President's continuing attacks on Attorney-General Jeff Sessions, Mr. Trump may need to reach out to the very Democrats he has excoriated in recent days. Even as he considers refusing to provide the health-care payments for insurers that are due in three weeks, he has hinted that he would eventually welcome Democrats to the health-care bargaining table.

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Shortly after the health-care effort failed, Republican Senator Pat Toomey of Pennsylvania, a strong conservative who has a record of seeking rapprochement with his party's rivals, said he was eager to see what Democrats might offer to address the Obamacare funding crisis. His Democratic colleague from Pennsylvania, Robert Casey Jr., issued a statement saying it was "now time for Democrats and Republicans to work on common-sense solutions that will make our health-care system more affordable and bring down costs." These two remarks from Pennsylvania lawmakers may provide the cracks that, as the late Canadian poet Leonard Cohen put it in his song Anthem, show "how the light gets in."

Mr. Trump has been willing to return to health-care even when it seemed dead the first time. Though he has vowed to "let Obamacare implode," he may yet try to revive it.

But in the meantime, one of the President's top priorities will soon be the subject of serious congressional consideration. It is a massive investment in infrastructure programs, from bridges and tunnels to airports – and it is an initiative certain to attract Democratic support.