"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.
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.