Mitt Romney has vowed that on his first day as president, he would act to repeal President Obama’s health-care law, thus fulfilling a long-standing promise.

But the reality for a President Romney would be more complicated.

Unless Republicans gain huge numbers in Congress, he probably would not have the votes to simply repeal the entire law.

From the White House, he could instruct the Department of Health and Human Services to drag its feet, pushing back deadlines and turning to an army of lawyers and consultants to figure out how to exploit the law’s weaknesses. But that kind of administrative muscle flexing could bring its own political problems.

“The simple answer is there’s nothing Romney can do on the first day to repeal the Affordable Care Act, but he could do a great deal to gum up the works,” said Timothy Jost, a law professor at Washington and Lee University.

Nearly two weeks after the Supreme Court upheld most of the law, its future remains unsettled, with the November election its next major hurdle. Americans have been stubbornly divided over the law, with Republican voters highly unified in their opposition to the largest new federal social program in decades.

In what has become a common Washington ritual, House Republicans are scheduled again Wednesday to vote on a repeal of the law. It will be the 33rd time Republicans have tried to undo all or part of the law since its passage in 2010 and the first since the court decision. As in those previous attempts, it is almost purely symbolic because it is unlikely to pass muster in the Democratic-led Senate.

Despite Romney’s role in passing a similar overhaul while governor of Massachusetts, he has been steadfast in his opposition to the law, a factor that has been key to his winning over deeply conservative voters.

As a result, many predict that he would move decisively and aggressively to make good on that promise if elected. Still, doing so would carry political pitfalls because millions of Americans not only support the law, but also are already benefiting from some of its provisions, such as one that requires insurance companies to cover children with preexisting conditions.

Others say Romney would be held responsible for the health-care system that might be reshaped by his actions.

“He belongs to a very conservative party that hates this bill, many members of which have sworn that they’d rather eat ground glass than let this law go forward,” said Henry J. Aaron, a senior fellow of economic studies at the Brookings Institution. “But there is the conflicting problem of, ‘If you break it, you own it.’ [He will own] anything that goes wrong with the health-care system down the road.”

Then there is the matter of what Romney would be able to do as president.

He has said that on Day One in office, he will “act to repeal Obamacare” and issue waivers to all 50 states exempting them from the law’s requirements. But neither will be so easy to pull off.

Few political analysts expect the GOP to have a 60-vote, filibuster-proof majority in the Senate come January, the advantage needed to pass most controversial legislation these days. Without it, Romney would have little chance of pushing a repeal bill through Congress.

Romney also would face problems in waiving all states from the measure. Although the law permits states to apply for exemptions, they must prove that they have alternate programs in place to provide comparable benefits. But those waivers won’t be available until 2017, according to experts.

Romney campaign officials say they have a blueprint.

“Governor Romney’s Day One plan includes an executive order instructing federal agencies to return maximum possible authority to the states,” spokeswoman Andrea Saul said in an e-mail. “This will include as much flexibility as the law permits, including waivers wherever possible under the law. He will then begin the work of fully repealing Obamacare and replacing it with common-sense reforms that will ensure Americans have access to the highest quality health care in the world.”

Without Congress, Romney could ask federal agencies to slow down implementation and turn off funding spigots. In cases in which the law remains ambiguous — for example, who would be exempt from the requirement that all Americans buy health insurance — he could instruct officials to write the regulations in a way that exempts the largest number of people.

But it is unclear whether such tactics would have a broad impact.

“A Mitt Romney presidency would be very unhelpful to the Affordable Care Act, no doubt about it,” said Neera Tanden, president of the left-leaning policy group Center for American Progress and a former Obama adviser. “He could make implementation difficult in a lot of ways, but I don’t think he can just not [implement the law].”

A better scenario for Romney would be if Republicans control both chambers of Congress. Even without a filibuster-proof majority in the Senate, Republicans could use a process called “reconciliation” to repeal parts of the bill that relate to spending. That could carve out such significant portions as the government subsidy that helps poor people buy the mandatory insurance and the penalty levied against people who don’t comply with the mandate.

“What he could do even if he does not have the 60 votes in the Senate, which seems unlikely, is use the budget process to repeal all of the portions of the Affordable Care Act that relate to spending money, which is where all the controversy is,” said Gail Wilensky, a senior fellow at Project HOPE who was a top health-care policymaker in both Bush administrations.