Republicans, buoyed by recent polls suggesting that their party could win the House and pick up seats in the Senate in November, are vowing to repeal or make major revisions in the health law that Democrats squeezed through Congress in March. But how difficult would it be to overturn that law?

“There might be a little bit of ‘barking dog catches car, doesn’t know what to do’ because it’s not like the aspects of the law that Republicans find objectionable can be excised cleanly and neatly like a tumor from the body, leaving the parts that might be more popular,” says Robert Reischauer, president of the Urban Institute, a nonpartisan Washington think tank, and former director of the Congressional Budget Office.

Due to the complexities involved, repeal of legislation as sweeping as the health law “almost never happens,” says Ross Baker, a political science professor at Rutgers University.

Yet Rep. Paul Ryan, R-Wis., is confident that the public will support a vigorous GOP attack on the sweeping health overhaul law that President Barack Obama and Democrats tout as a signature policy achievement of the president’s first term. He acknowledged that it will be difficult to make changes since Obama has the authority to veto legislation. “We’ve got to figure out how to do that with the current occupant in the White House,” Ryan says.

Here’s a guide to what could be in store if Republicans call the shots:

*Repeal And Replace

If Republicans win back the House they will control what legislation comes before the chamber. Ryan said his party must develop an alternative to the health law and then sell that package to the public.

“The question is, what can you do about [the health law] if we have divided government? I think we need to make the case for what we would replace it with,” he says. “We need to give the country an alternative system that’s fiscally responsible, one that gives patients ownership and choice and one that does not create brand new entitlements.”

House Energy and Commerce Committee Chairman Henry Waxman, D-Calif., says Ryan and his colleagues will face opposition not only from Obama and Democrats but also from the public if the GOP tries to weaken the health law.

“I think it will be very difficult for them to try to repeal the health care bill in whole or in part, especially when the American people see what’s happening,” Waxman says. “Are they going to repeal the assistance to small business to cover their employees? Are they going to try to strike some of the funding that’s available for subsidies for low-income people?”

If House Republicans prevail in their repeal efforts, prospects for passage in the Senate are dim even if the GOP takes control of that chamber, which seems unlikely. No matter who wins in the Senate, the margin between the parties will probably be very small. Legislation as combative as trying to repeal part or all of the health care law would most surely need 60 votes to pass, requiring the Republicans, who now control 41 seats, win some Democratic support for any changes.

If the Republicans faced an Obama veto, they would need to gain support from two-thirds of both chambers to override it.

*Defund The Bill

Republicans could turn to the annual appropriations and budget process or push stand-alone bills to delay or stop funding for provisions of the law they dislike, including the individual mandate, the health insurance exchanges and the Medicaid expansion. They might also work to weaken provisions in the bill that deal with Medicare physician reporting requirements that some physicians find onerous and block the creation of a nonprofit research institute to examine the effectiveness of various medical treatments.

Mandatory funding, which comprises much of the health measure beginning in 2014, will continue unless Republicans can change current law, a heavy lift considering such initiatives would have to pass both the House and Senate and win Obama’s signature. Discretionary funding must be approved each year but differences between House and Senate versions of appropriations measures must be ironed out and that generally produces a compromise package.

A major problem with the defunding strategy is that since so much of the bill is inter-related, trying to dismantle it piecemeal could lead to unintended consequences. The GOP could also find itself with more than it bargained for, says Reischauer.

While the individual mandate is unpopular, “you can’t pull it out of the law without all sorts of other elements falling apart,” Reischauer says. And scrapping the mandate, which requires most people to have coverage or pay a penalty, would anger health insurers — a core GOP constituency.

Insurers have agreed to abide by new consumer protections, such as not denying coverage based on a pre-existing medical condition, in exchange for 32 million new customers. Hospitals agreed to payment cuts on the premise that more people would have health care and hospitals would have less uncompensated care.

More insured people would create additional demand for services from hospitals and other health care providers and manufacturers, such as medical device makers, helping to offset new taxes and federal payment cuts. If Republicans try to reduce the amount of subsidies given to individuals to purchase health insurance or they change the Medicaid expansion, more people could be left uninsured.

“Everything is connected to everything else in health reform legislation,” Reischauer says. “And so picking and choosing, tinkering around the edges, isn’t as easy when you’re writing the legislation as it is when you’re giving the campaign speech.”

Some Republicans, such as Rep. Lynn Westmoreland, R-Ga., have suggested that if Republicans can’t repeal the entire law or portions of it, they may simply refuse to negotiate with Democrats or Obama over spending bills – including those for agencies that are responsible for implementing the health care law – resulting in a replay of the 1995 government shutdown.

If that happens, Rep. Rob Andrews, D-N.J., says that “people are going to have a very hard time trying to understand why their Social Security checks aren’t being mailed out because of some abstract debate about the free market in health care.”

And the idea of a government shutdown is not relished in all parts of the Republican Party. Days after Westmoreland’s remarks, House Minority Leader John Boehner, R-Ohio, said the GOP’s goal is to reduce the size of government, not shut it down.

*Oversight Showdown

Republican rule in either chamber will guarantee an onslaught of confrontational oversight hearings, with GOP leaders demanding frequent Capitol Hill appearances by officials from the White House, the Department of Health and Human Services and the Centers for Medicare and Medicaid Services (CMS), and other federal agencies that are implementing the law.

Republicans could use the sessions to highlight provisions that they oppose, such as the requirement that most individuals purchase health insurance. GOP leaders could also scrutinize the regulatory process of implementing the bill and be aided by players in the health care industry – insurers for example – that want less restrictive regulations.

Republicans may also hold hearings on a new board created in the health law to make recommendations on how to reduce Medicare spending growth beyond certain targets, or the GOP could highlight the law’s new taxes and fees. Republicans in both chambers have sought to have CMS administrator Donald Berwick testify on the health law’s changes to Medicare program and to answer questions about statements he has made in support of the British health care system.

“When you can’t achieve the ultimate objective, which of course would be repeal, what you can do is inflict as much pain as possible on the people you hold responsible for it,” said Baker. “Just being able to haul somebody in front of a committee under the threat of subpoena, for example, or contempt of Congress, and working them over in public is enormously satisfying.”

Democrats say that such an aggressive oversight campaign would sap the time and resources of agencies now fully focused on implementing the health law. Hours would be needed to prepare and write testimony, answer numerous inquiries from congressional committees of jurisdiction and other members.

Even if the efforts have no measurable impact – like repealing all or portions of the law – they could reinforce the party’s message that the law will do more harm than good.

“Whether or not you might be successful in repealing either all or part of [the law] may be less important than the fact that you can go in front of voters and say we did our best and we’ll try again,” Baker said. “This has been done by both sides for years.”