The Fed lending program to help banks pay depositors is backed by 25 billion of taxpayer funds that would cover any losses on the loans. But the Fed says it is unlikely that the money will be needed because the loans will be backed by Treasury bonds and other safe securities as collateral. Also will point out this is not 2008 since Biden has stressed that the banks managers will be fired and their investors will not be protected. Both banks will cease to exist. In the 2008 crisis, some financial institutions that received government financial aid, like the insurer AIG, were rescued from bankruptcy. (culled from AP this morning)
And stopping a run on other banks is what any POTUS would do, and hardly Bank Medicare. And those measures are being funded by the banks paying in to an FDIC special insurance assessment.
I think this administration will take a hard look at legislation to go after undercapitalized institutions.