Instead, GOP lawmakers cite recent announcements that some insurance companies will retain a few of the law's higher-profile provisions as evidence that quick legislative action is not essential. Those are steps that officials say Republicans quietly urged in private conversations with the industry.
Once the Supreme Court issues a ruling, "the goal is to repeal anything that is left standing," said Sen. John Barrasso, R-Wyo., a member of the party's leadership.
Beyond that, "we ought to go step by step to lower the cost" of health care, he added, a formula repeated by numerous other Republicans interviewed in recent days.
Across the political aisle, neither President Barack Obama nor congressional Democrats have said how they will react to a high court ruling that could wipe out the legislation they worked so hard to enact.
"We're not spending a whole bunch of time planning for contingencies," Obama said this spring at the annual meeting of The Associated Press. He expressed confidence the court would uphold the law, and neither he nor his aides have said what fallback plans are under discussion. "We will be prepared in any eventuality," White House aide David Plouffe said Sunday on ABC's "This Week," although he declined to elaborate.
Among Republicans, aides to Speaker John Boehner, Senate Republican leader Mitch McConnell and other key lawmakers have convened a series of meetings in recent weeks to plan a post-ruling strategy.
A Supreme Court ruling is expected within the next two weeks on a challenge to the law, which has drawn fierce opposition among most Republicans for its requirement that most individuals carry health insurance.
While three big insurance companies announced plans this past week to retain certain protections for an estimated 40 percent of all individuals who receive their coverage through work, there has been no advance word from the drug industry on how prescription costs for older people might be affected by a finding that the law is unconstitutional.
Even so, Republicans say they have no plans for assuring continuity of a provision that reduces out-of-pocket costs for seniors with high drug expenses. This coverage gap is known as "doughnut hole."
"I don't think anybody intends to get involved" in the portion of Medicare that provides prescription drug coverage. The program is "working better than we designed it," said Sen. Richard Burr, R-N.C., referring to studies that show the program's cost is lower than was originally estimated.
The drug industry has yet to disclose its plans.
House Republicans have voted 30 times to eliminate, defund or scale back parts or all of the health law, most recently approving a measure to wipe out a tax on medical devices.
Senate Democrats have blocked nearly all of the previous attacks. Forcing another vote would allow Republicans to signal a continued commitment to supporters of repeal, while simultaneously requiring Democrats to take another stand on a measure that has failed to generate significant public support and might by then also have been found deficient by the Supreme Court.
"Democrats don't want to talk about health care between now and the election, especially Obamacare," said Don Stewart, a spokesman for McConnell, referring to the law signed in 2010.
Many members of the GOP rank and file campaigned on a motto of "repeal and replace" in 2010 when it came to the law. But now, nearly two years later, they express no urgency to replace a law drafted by Democrats, and one they hope the court will kill, with a different one of their own.
"We're not going to repeat the mistakes made by the Democrats who run Washington when they passed a 2,700-page bill that no one had actually read," said Michael Steel, a spokesman for Boehner, R-Ohio.
While Republicans say the recent insurance industry announcements eased the political pressure on them to act, some cited other reasons for moving carefully on replacement legislation.
With the party united around repeal of the existing law, they said they want to avoid an internal squabble over the details of any replacement legislation, at least until after the elections this fall.
In addition, they want to wait until they know whether GOP presidential candidate Mitt Romney wins the White House in November.
Romney has provided few details about his plans for health care legislation. He supports repeal of the current law, in part citing a requirement for individuals to obtain coverage, even though as governor of Massachusetts he signed a law with a similar provision.
On one big-ticket item, Romney and House Republicans already have parted company.
Both criticize Obama and Democrats for cutting Medicare by $500 billion over the next decade as part of the health care law.
But Romney's aides say he wants to restore the money to Medicare, while the budget that the Republicans pushed through the House would instead put the money toward deficit reduction.
In interviews, several Republicans drew attention to recent announcement from a few insurers pledging to retain some recent changes regardless of a court ruling.
UnitedHealth Group, Humana and Aetna said that regardless of the court's ruling, they will continue to cover preventive care such as immunizations and screenings without requiring a copayment. They also said children up to age 26 may be covered through their parents' insurance plans.
Additionally, UnitedHealth Group Inc. and Humana Inc. said they will not reimpose lifetime dollar limits on benefits, a provision most important for patients with cancer and other expensive-to-treat diseases.
The actions left in question the fate of other provisions in the health care law, including a requirement for new coverage for children up to age 19 with existing medical conditions.
Nor do the voluntary announcements cover everyone.
United Health and Humana said their announcements would affect customers with individual policies and those who receive small-group coverage through work.
Workers and families who receive coverage from large employers that pay their own medical claims are unaffected. Those employers will make their own decisions how to respond to the court's ruling.
Neither company provided an estimate of how many of their customers would be affected by their announcement.
The nonpartisan Kaiser Family Foundation estimates that 60 percent of covered workers are in plans that are self-funded by their employers.