But as Republicans in the Senate press ahead with legislation that would dramatically cut Medicaid and scale back the Affordable Care Act marketplaces, it is increasingly clear that President Trump is almost certain to fall well short of fulfilling those promises.
Trump and congressional Republicans will likely hail any bill that reaches the president's desk as the fulfillment of a long-standing pledge to "repeal and replace" the ACA, former president Barack Obama's signature health-care law. But if the House and Senate agree on legislation along the lines of what is now being debated, millions — including some of Trump's most ardent supporters — are projected to lose coverage, receive fewer benefits or see their premiums rise.
And if the health-care push stalls or falls apart, the president who campaigned for the White House as the ultimate dealmaker will be dealt a serious political blow — another example of Trump's inability to move major legislation through Congress.
"He's going to own it either way, whether he signs a bill or doesn't get a bill," said Michael Steele, the former chairman of the Republican National Committee. Steele said passage of the legislation could hurt Trump politically as much as its failure. "You're going to have a whole generation of people who had health care losing health care, and in many instances, they're Trump voters. I think that's a very risky play."
Over the weekend, Trump acknowledged that he had called the House bill "mean" weeks after celebrating its passage in the Rose Garden. He suggested other changes could be coming to the Senate bill to ease its impact on lower-income Americans but said "we have a very good plan" that he characterized as close to passing.
By Monday, he seemed to be preparing to blame others if it failed.
"Republican Senators are working very hard to get there, with no help from the Democrats," Trump said in a tweet. "Not easy! Perhaps just let OCare crash & burn!"
One bright spot for Trump is that many of his most die-hard backers echo the president in largely blaming others for continued gridlock in Washington. At least for now, many believe that he would fulfill his promises on health care and other priorities if only he were given the chance.
Charlene Beatty, 71, who lives on an eastern Iowa farm and attended Trump's rally last week in Cedar Rapids, said Congress needs to stop obsessing over the investigation into Russian meddling in the election and accomplish some of the things Trump has asked the lawmakers to do — including reforming health care.
GOP senators say their bill took steps to rectify some issues in a House version of the measure, which would cause an estimated 23 million more people to be uninsured in the coming decade, according to an analysis by the nonpartisan Congressional Budget Office.
But a CBO estimate Monday said nearly as many — 22 million — would be uninsured under the Senate bill.
That means that managing expectations could be one of Trump's biggest challenges in coming weeks.
Many Republicans, even those supportive of the effort to "repeal and replace" the ACA, view it as only a starting point for fixing the problems facing the health-care industry.
"He's got to help make the American people understand that this is not the end of the road," Grace-Marie Turner, president of the Galen Institute, a conservative health-care think tank, said. "It's something they have to do to break the logjam, but they're going to be passing other bills as well."
Earlier in the debate, the Trump administration stressed that it plans to push other reforms besides the pending legislation to provide consumers more choices of health-care plans, among other objectives.
In the shorter term, Trump has cast congressional action as a necessary step to stave off collapse of the ACA.
"#Obamacare is dead," Trump said in a tweet on Sunday. "Insurance markets are collapsing & millions don't have choices. Americans deserve better."
Analysts say that the bill could leave middle-income people and the poor with too little support to pay health-care costs and that cuts to Medicaid funding in later years could leave the elderly particularly vulnerable. The legislation also phases out federal support for a Medicaid expansion that was a key provision of Obama's initiative.
That phaseout and several other key provisions do not take effect immediately, which could limit the short-term political impact on Trump and congressional Republicans.
Some boosters say the legislation is the start of an effort to make good on Trump's promise of market-based universal coverage. They point to the flexibility the bill offers to states, tax credits to assist with health-care costs and regulatory relief for insurers, which they argue could help bring greater competition to the health insurance marketplace.
"Conservatives should embrace the goal of universal coverage, and this bill makes enormous progress towards that goal," said Avik Roy, a health-care expert who was critical of the House bill but supports the Senate's version.
"Does this bill have heart?" Roy asked, citing a standard Trump recently articulated. "It absolutely does."
Polls suggest Trump has a long way to go to make that case to voters.
Only 16 percent of adults believe that House bill is a good idea, while 48 percent say it's a bad idea, according to an NBC News/Wall Street Journal poll released last week. Even Republican respondents are lukewarm, with 34 percent viewing the bill positively and 17 percent viewing it negatively.
Doug Heye, a Republican consultant, argued that the president badly needs a legislative victory and that achieving a high-profile win should override concerns about the legislation's impact.
"Those who are strong Trump supporters have remained so despite the controversies," Heye said. "They still see Trump as someone willing to take on their fights."
Interviews with Trump supporters who attended his campaign rally in Cedar Rapids suggest that many of them are dissatisfied with their health care — and many suspect Trump won't fully deliver on his promises. But so far, they don't seem inclined to blame him.
Crystal Beckler, 54, of Crawfordsville, Iowa, said she has a private health insurance plan through a broker for herself and her husband, a self-employed truck driver. But she said few services are covered and she ends up paying for many things out of pocket, making her wonder why she even has insurance.
"He's on it," Beckler said of Trump, "if they would just work with him."
Jim Slage, who drove with his wife more than five hours from their home in Lincoln, Neb., to Cedar Rapids for Trump's rally, said that he has insurance through his job as a truck driver but that costs have gone up while quality has fallen. Copays used to be $20 and are now $60, he said, and it seems like fewer things are covered by the insurance company.
The couple said they have friends who have insurance plans through the government marketplace and are paying monthly premiums that are higher than their monthly rent or mortgage. The Slages said that while the congressional plans to scale back Obamacare still don't accomplish all of the things that Trump promised, they still hope he can improve upon that.
"I hope so," Slage said.
"God, I hope so," Bernice Slage added.
Angie Hanzelka, 47, voted for Trump and, so far, has been impressed with everything that he has accomplished "in a very short period of time." But she said she's worried about health care.
Hanzelka, a bartender who lives in Cedar Rapids, has health insurance she bought through the government marketplace that costs $300 per month and has a $7,000 deductible.
She wants her monthly premium and deductible to go down and more plans from which to choose, all of which Trump has promised to do. But she worries that her coverage could become even more expensive under the Republican plan.
Democratic strategists argue that some Trump voters will eventually sour on him if the health-care bill becomes law, and that it's likely to make it harder for Trump to expand his appeal.
"It's hurting the people who voted for him, and they will come to see that," said Mary Anne Marsh, a Boston-based Democratic consultant.
Trump has been vocal about his hope that he might have started his tenure by tackling tax reform instead of health care. But now his entire agenda is bogged down by the effort.
Given the potential consequences of the bill, some Republicans suggest failure would be the best outcome for Trump at this point. "I don't think he realizes that," said John Weaver, who was chief strategist for the 2016 presidential campaign of Gov. John Kasich (R-Ohio). "There's a bigger downside if it passes and millions of people lose coverage."
Johnson reported from Cedar Rapids, Iowa.