Receivership [0]. Note that if your bank closes, the FDIC still sends you your money.
> How long would that last in such a scenario?
The FDIC has about $7 trillion in insured deposits [1].
In the crisis, between TARP [2] and TALF [3], the federal government printed $1.5 trillion. (About $1.8 trillion in 2017 dollars [4].) Meanwhile, the Fed bought $4.5 trillion in assets through its quantitative easing programmes [5].
Adjusting for inflation, we probably saw close to $7 trillion in fiscal and monetary stimulus.
[0] https://www.fdic.gov/about/strategic/strategic/receivership....
[1] https://www.fdic.gov/bank/statistical/stats/2017jun/fdic.pdf
[2] https://en.m.wikipedia.org/wiki/Troubled_Asset_Relief_Progra...
[3] https://en.m.wikipedia.org/wiki/Term_Asset-Backed_Securities...
[4] https://data.bls.gov/cgi-bin/cpicalc.pl?cost1=1.50&year1=200...
The FDIC (a) cannot "cram down" [1], (b) has the ability to borrow $500 billion from the U.S. Treasury [2] and (c) is backed by the "full faith and credit" of the U.S. Government [3]. A decision to "renumerate small a fraction [sic] of insured deposits" would be a political call. It's certainly not a "could only" scenario.
[1] https://en.wikipedia.org/wiki/Cram_down
[2] https://www.fdic.gov/news/news/press/2009/pr09153.html
[3] https://www.fdic.gov/deposit/deposits/