Hatch said that while Obamacare has hurt millions of people and needs to be ultimately repealed and replaced, Congress should do something in the meantime to mitigate the effects if the high court decides to invalidate that financial aid.
"I don't think we can stand by and simply let the shortcomings of the law hurt people more," he said during a speech at the Heritage Foundation in Washington, D.C.
Read MoreGov't sent 800K customers wrong Obamacare tax info
"In the coming days, I will release details of a short-term solution for Americans who may be affected," Hatch said. "That solution will address immediate concerns and set the stage for a permanent solution in the future."
Hatch's promise reveals a potentially tricky political situation for Republicans.
The GOP opposes Obamacare and backs the case challenging the HealthCare.gov subsidies. But there is concern that elected Republicans will suffer a backlash if Obamacare customers lose their health coverage, particularly if Congress does not come up with an alternative to the current subsidy structure.
At issue is the financial assistance given to nearly 9 in 10 customers of HealthCare.gov, the federally run Obamacare exchange that serves 37 states.
Read MoreObamacare a bargain? It is for these Americans
Plaintiffs in the case known as King vs. Burwell claim that those subsidies are not legal because the ACA only explicitly authorizes such financial assistance for customers of an Obamacare insurance exchange run by an individual state, not by the federal government.
The Obama administration argues the subsidies are legal, and says Congress' intent was to provide the subsidies to all Obamacare customers, not just to ones who lived in a state that set up its own exchange.