WASHINGTON — The legal campaign to destroy President Obama’s health care law may be nearing its conclusion, but as the Supreme Court deliberates over the law’s fate, the search for a replacement by Republican lawmakers is finally gaining momentum.

Senior Republicans in Congress hope that by June, the Supreme Court will invalidate the subsidies that 7.5 million Americans in 34 states have been given to purchase health insurance through the federal website Healthcare.gov. But the prospects of legal victory have also raised practical and political fears that Republicans will take the blame for the health care crisis that would follow.

A legislative scramble is underway. On Monday, Representatives Paul D. Ryan of Wisconsin, Fred Upton of Michigan and John Kline of Minnesota, the chairmen of the powerful committees that control health policy, proposed what they called an “off ramp” from the Obama health act that would let states opt out of the law’s central requirements.

On the other side of the Capitol, Senators John Barrasso of Wyoming, Lamar Alexander of Tennessee and Orrin G. Hatch of Utah, all Republicans, offered their own plan this week to provide temporary assistance to those who would lose their subsidies and new freedom to all states to redesign their health care marketplaces without the strictures and mandates of the health care law.