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The administration is still writing the rules for fully implementing the law, including how states will run their health care exchanges designed to make coverage affordable. But the law has already established new protections for consumers, such as lifting the lifetime cap on benefit payments, allowing young adults to stay on their parents’ policies and preventing insurance companies from denying coverage based on pre-existing health problems.

Administration officials said the changes Mr. Obama is supporting are unlikely to have any effect on the lawsuits over the law’s constitutionality. Two federal judges have struck down part or all of the law, while three others have upheld it, with a Supreme Court review of the law considered certain.

But pushing for changes to the law is likely to add to the fight on Capitol Hill, where the House Republican majority has passed bills to repeal the entire law and to starve it of funding.

Senate Democrats have blocked the repeal bill and have said they will reject efforts to cut off funding for implementation, too.

Still, the changes Mr. Obama endorsed Monday would require congressional approval, and that could reopen many of those debates in Congress. The House floor this week is scheduled to consider the bill to repeal the tax-reporting requirement.

Stephen Dinan contributed to this report.