At this point, I think Biden's administration is banking on and hoping the courts shoot down the mandate.
It's obviously going to tank the economy further and destroy the midterms.
The only play they have remaining is this one:
"Those big meanies in the Supreme Court stopped our plan that was the only way to stop covid! The fact that it's still around is all due to the unvaccinated people who would have taken the vax if it was mandated. The GOP thwarted our ability to commit to any of our plans and our only hope is that with another Democratic term we can stack the courts so this never happens again. The economy and supply chains are in shambles because covid has killed so many workers, of course, and that would have been avoided if not for Republicans, so blame them for the breadlines."
Is it a longshot? Yes, the Democrats are polling terribly right now and I know so many people who have walked away from Democrat party-line voting that I expect a massacre no matter what spin they try to put on this disastrous presidency. But no way are they going to take responsibility for the mess they've created. They need obstructionism from the conservative wing of the court if they want to have a snowball's chance in hell of coming back from this in the next decade. Without a scapegoat to point to, it's all looking bad.