It could also pass a separate law extending some form of financial assistance to those currently receiving subsidies, while extracting some further concessions from Democrats to craft Obamacare more to their liking. Most of the GOP plans that have been proposed do this: Sen. Ron Johnson's bill, for example, extends the subsidies while repealing the law's employer and individual mandates.
In theory, Congress could also pass a full "repeal and replace" law, gutting Obamacare and establishing an entirely new health care system in its place. But Obama's veto pen looms.
Why it will act: Because no one—Democrat or Republican—wants millions of people to lose their health coverage. Morality aside, the fallout could also have political consequences if the public blames the GOP for the lawsuit and/or Congress for failing to act. Neither party wants it held against them in the 2016 election.
Why it won't: Because the fierce partisanship that has always surrounded Obamacare will prevent any solution from being passed. Republicans will refuse to do a simple fix, because that would mean allowing Obamacare to continue as is, and Democrats won't concede central elements of the legislation.
What it could do: To be determined.
The question of how much freedom the administration has to act is already controversial. The White House has insisted from the beginning that there wouldn't be an easy administrative fix.
"We can't undo the massive damage," Health and Human Services Secretary Sylvia Mathews Burwell said recently.
But some outside observers have theorized that the administration could actually do a lot to clean up the King mess on its own (and has been hiding its cards to pressure the Court).
The specifics vary, but the hypothetical plan looks something like this: HHS makes it as easy as possible for states to "establish" an exchange and restart the subsidies. Maybe the governor just signs a piece of paper; maybe the administration "rents" HealthCare.gov to them.
Nicholas Bagley, a law professor at the University of Michigan who supports the White House's view of the case, even theorized that the administration could interpret many states to have already "established" an exchange without doing anything additional.
Why it will act: Because it would allow the White House to avoid negotiating with Congress and giving up concessions, or risking that lawmakers fail to act.
Why it won't: Because it legally can't. The ACA details some very specific things that states need to do to establish an exchange, and HHS might not have the interpretive leeway. Plus, it would require buy-in from the affected states, the majority of which are controlled by Republicans.
What they could do: Set up an exchange.
The King case is a problem for the administration only because not every state established its own exchange, as many initially assumed they would. If states that don't already have exchanges decide to set one up, the subsidies start flowing again.